Random Fields on the Sphere :: Representation, Limit Theorems and Cosmological Applications.
Reviews recent developments in the analysis of isotropic spherical random fields, with a view towards applications in cosmology.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2011.
|
| Schriftenreihe: | London Mathematical Society Lecture Note Series, 389.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Reviews recent developments in the analysis of isotropic spherical random fields, with a view towards applications in cosmology. |
| Beschreibung: | 7.6.1 Convolutions as mixed states. |
| Beschreibung: | 1 online resource (355 pages) |
| Bibliographie: | Includes bibliographical references (pages 326-337) and index. |
| ISBN: | 9781139117487 1139117483 1283296179 9781283296175 9780511751677 0511751672 9781139128148 1139128140 1139115316 9781139115315 9781139113120 1139113127 |
Internformat
MARC
| LEADER | 00000cam a2200000Mi 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn769341761 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr |n|---||||| | ||
| 008 | 111226s2011 enk ob 001 0 eng d | ||
| 040 | |a EBLCP |b eng |e pn |c EBLCP |d OCLCQ |d DEBSZ |d IDEBK |d OL$ |d OCLCO |d OCLCQ |d OCLCO |d CDX |d OCLCF |d N$T |d E7B |d YDXCP |d UIU |d REDDC |d CAMBR |d OSU |d OCLCQ |d UAB |d OCLCQ |d INT |d AU@ |d OCLCQ |d UKAHL |d OCLCO |d OCLCQ |d OCLCO |d OCLCL | ||
| 066 | |c (S | ||
| 019 | |a 759007197 |a 761284104 |a 768771958 |a 816866945 |a 819630810 |a 853654206 |a 1178961534 | ||
| 020 | |a 9781139117487 | ||
| 020 | |a 1139117483 | ||
| 020 | |a 1283296179 | ||
| 020 | |a 9781283296175 | ||
| 020 | |a 9780511751677 |q (electronic book) | ||
| 020 | |a 0511751672 |q (electronic book) | ||
| 020 | |a 9781139128148 |q (electronic bk.) | ||
| 020 | |a 1139128140 |q (electronic bk.) | ||
| 020 | |a 1139115316 |q (electronic bk.) | ||
| 020 | |a 9781139115315 |q (electronic bk.) | ||
| 020 | |z 0521175615 | ||
| 020 | |z 9780521175616 | ||
| 020 | |a 9781139113120 |q (e-book) | ||
| 020 | |a 1139113127 | ||
| 035 | |a (OCoLC)769341761 |z (OCoLC)759007197 |z (OCoLC)761284104 |z (OCoLC)768771958 |z (OCoLC)816866945 |z (OCoLC)819630810 |z (OCoLC)853654206 |z (OCoLC)1178961534 | ||
| 050 | 4 | |a QA406 .M37 2011 | |
| 072 | 7 | |a PBT |2 bicssc | |
| 072 | 7 | |a SCI |x 015000 |2 bisacsh | |
| 082 | 7 | |a 523.101/5195 | |
| 084 | |a MAT029000 |2 bisacsh | ||
| 049 | |a MAIN | ||
| 100 | 1 | |a Marinucci, Domenico. | |
| 245 | 1 | 0 | |a Random Fields on the Sphere : |b Representation, Limit Theorems and Cosmological Applications. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2011. | ||
| 300 | |a 1 online resource (355 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society Lecture Note Series, 389 ; |v v. 389 | |
| 505 | 0 | |6 880-01 |a Cover; Title; Copyright; Contents; Dedication; Preface; 1 Introduction; 1.1 Overview; 1.2 Cosmological motivations; 1.3 Mathematical framework; 1.4 Plan of the book; 2 Background Results in Representation Theory; 2.1 Introduction; 2.2 Preliminary remarks; 2.3 Groups: basic definitions; 2.3.1 First definitions and examples; 2.3.2 Cosets and quotients; 2.3.3 Actions; 2.4 Representations of compact groups; 2.4.1 Basic definitions; 2.4.2 Group representations and Schur Lemma; 2.4.3 Direct sum and tensor product representations; 2.4.4 Orthogonality relations; 2.5 The Peter-Weyl Theorem. | |
| 505 | 8 | |a 3 Representations of SO(3) and Harmonic Analysis on S23.1 Introduction; 3.2 Euler angles; 3.2.1 Euler angles for SU(2); 3.2.2 Euler angles for SO(3); 3.3 Wigner's D matrices; 3.3.1 A family of unitary representations of SU(2); 3.3.2 Expressions in terms of Euler angles and irreducibility; 3.3.3 Further properties; 3.3.4 The dual of SO(3); 3.4 Spherical harmonics and Fourier analysis on S2; 3.4.1 Spherical harmonics and Wigner's Dl matrices; 3.4.2 Some properties of spherical harmonics; 3.4.3 An alternative characterization of spherical harmonics; 3.5 The Clebsch-Gordan coefficients. | |
| 505 | 8 | |a 3.5.1 Clebsch-Gordan matrices3.5.2 Integrals of multiple spherical harmonics; 3.5.3 Wigner 3 j coefficients; 4 Background Results in Probability and Graphical Methods; 4.1 Introduction; 4.2 Brownian motion and stochastic calculus; 4.3 Moments, cumulants and diagram formulae; 4.4 The simplified method of moments on Wiener chaos; 4.4.1 Real kernels; 4.4.2 Further results on complex kernels; 4.5 The graphical method for Wigner coefficients; 4.5.1 From diagrams to graphs; 4.5.2 Further notation; 4.5.3 First example: sums of squares; 4.5.4 Cliques and Wigner 6 j coefficients. | |
| 505 | 8 | |a 4.5.5 Rule n. 1: loops are zero4.5.6 Rule n. 2: paired sums are one; 4.5.7 Rule n. 3: 2-loops can be cut, and leave a factor; 4.5.8 Rule n. 4: three-loops can be cut, and leave a clique; 5 Spectral Representations; 5.1 Introduction; 5.2 The Stochastic Peter-Weyl Theorem; 5.2.1 General statements; 5.2.2 Decompositions on the sphere; 5.3 Weakly stationary random fields in Rm; 5.4 Stationarity and weak isotropy in R3; 6 Characterizations of Isotropy; 6.1 Introduction; 6.2 First example: the cyclic group; 6.3 The spherical harmonics coefficients; 6.4 Group representations and polyspectra. | |
| 505 | 8 | |a 6.5 Angular polyspectra and the structure of?l1 ... ln6.5.1 Spectra of strongly isotropic fields; 6.5.2 The structure of?l1 ... ln; 6.6 Reduced polyspectra of arbitrary orders; 6.7 Some examples; 7 Limit Theorems for Gaussian Subordinated Random Fields; 7.1 Introduction; 7.2 First example: the circle; 7.3 Preliminaries on Gaussian-subordinated fields; 7.4 High-frequency CLTs; 7.4.1 Hermite subordination; 7.5 Convolutions and random walks; 7.5.1 Convolutions on?SO (3); 7.5.2 The cases q = 2 and q = 3; 7.5.3 The case of a general q: results and conjectures; 7.6 Further remarks. | |
| 500 | |a 7.6.1 Convolutions as mixed states. | ||
| 520 | |a Reviews recent developments in the analysis of isotropic spherical random fields, with a view towards applications in cosmology. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references (pages 326-337) and index. | ||
| 650 | 0 | |a Compact groups. |0 http://id.loc.gov/authorities/subjects/sh85029280 | |
| 650 | 0 | |a Cosmology |x Statistical methods. | |
| 650 | 0 | |a Random fields. |0 http://id.loc.gov/authorities/subjects/sh85111347 | |
| 650 | 0 | |a Spherical harmonics. |0 http://id.loc.gov/authorities/subjects/sh85126596 | |
| 650 | 6 | |a Groupes compacts. | |
| 650 | 6 | |a Cosmologie |x Méthodes statistiques. | |
| 650 | 6 | |a Champs aléatoires. | |
| 650 | 6 | |a Harmoniques sphériques. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a SCIENCE |x Cosmology. |2 bisacsh | |
| 650 | 7 | |a Compact groups |2 fast | |
| 650 | 7 | |a Random fields |2 fast | |
| 650 | 7 | |a Spherical harmonics |2 fast | |
| 700 | 1 | |a Peccati, Giovanni, |d 1975- |1 https://id.oclc.org/worldcat/entity/E39PCjHW3xR6VdxggCgh4BRBT3 |0 http://id.loc.gov/authorities/names/n2011037471 | |
| 776 | 0 | 8 | |i Print version: |a Marinucci, Domenico. |t Random Fields on the Sphere : Representation, Limit Theorems and Cosmological Applications. |d Cambridge : Cambridge University Press, ©2011 |z 9780521175616 |
| 830 | 0 | |a London Mathematical Society Lecture Note Series, 389. | |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=399346 |3 Volltext |
| 880 | 0 | 0 | |6 505-01/(S |g Machine generated contents note: |g 1. |t Introduction -- |g 1.1. |t Overview -- |g 1.2. |t Cosmological motivations -- |g 1.3. |t Mathematical framework -- |g 1.4. |t Plan of the book -- |g 2. |t Background Results in Representation Theory -- |g 2.1. |t Introduction -- |g 2.2. |t Preliminary remarks -- |g 2.3. |t Groups: basic definitions -- |g 2.4. |t Representations of compact groups -- |g 2.5. |t Peter-Weyl Theorem -- |g 3. |t Representations of SO(3) and Harmonic Analysis on S2 -- |g 3.1. |t Introduction -- |g 3.2. |t Euler angles -- |g 3.3. |t Wigner's D matrices -- |g 3.4. |t Spherical harmonics and Fourier analysis on S2 -- |g 3.5. |t Clebsch-Gordan coefficients -- |g 4. |t Background Results in Probability and Graphical Methods -- |g 4.1. |t Introduction -- |g 4.2. |t Brownian motion and stochastic calculus -- |g 4.3. |t Moments, cumulants and diagram formulae -- |g 4.4. |t simplified method of moments on Wiener chaos -- |g 4.5. |t graphical method for Wigner coefficients -- |g 5. |t Spectral Representations -- |g 5.1. |t Introduction -- |g 5.2. |t Stochastic Peter-Weyl Theorem -- |g 5.3. |t Weakly stationary random fields in Rm -- |g 5.4. |t Stationarity and weak isotropy in R3 -- |g 6. |t Characterizations of Isotropy -- |g 6.1. |t Introduction -- |g 6.2. |t First example: the cyclic group -- |g 6.3. |t spherical harmonics coefficients -- |g 6.4. |t Group representations and polyspectra -- |g 6.5. |t Angular polyspectra and the structure of δl1 ... l1 -- |g 6.6. |t Reduced polyspectra of arbitrary orders -- |g 6.7. |t Some examples -- |g 7. |t Limit Theorems for Gaussian Subordinated Random Fields -- |g 7.1. |t Introduction -- |g 7.2. |t First example: the circle -- |g 7.3. |t Preliminaries on Gaussian-subordinated fields -- |g 7.4. |t High-frequency CLTs -- |g 7.5. |t Convolutions and random walks -- |g 7.6. |t Further remarks -- |g 7.7. |t Application: algebraic/exponential dualities -- |g 8. |t Asymptotics for the Sample Power Spectrum -- |g 8.1. |t Introduction -- |g 8.2. |t Angular power spectrum estimation -- |g 8.3. |t Interlude: some practical issues -- |g 8.4. |t Asymptotics in the non-Gaussian case -- |g 8.5. |t quadratic case -- |g 8.6. |t Discussion -- |g 9. |t Asymptotics for Sample Bispectra -- |g 9.1. |t Introduction -- |g 9.2. |t Sample bispectra -- |g 9.3. |t central limit theorem -- |g 9.4. |t Limit theorems under random normalizations -- |g 9.5. |t Testing for non-Gaussianity -- |g 10. |t Spherical Needlets and their Asymptotic Properties -- |g 10.1. |t Introduction -- |g 10.2. |t construction of spherical needlets -- |g 10.3. |t Properties of spherical needlets -- |g 10.4. |t Stochastic properties of needlet coefficients -- |g 10.5. |t Missing observations -- |g 10.6. |t Mexican needlets -- |g 11. |t Needlets Estimation of Power Spectrum and Bispectrum -- |g 11.1. |t Introduction -- |g 11.2. |t general convergence result -- |g 11.3. |t Estimation of the angular power spectrum -- |g 11.4. |t functional central limit theorem -- |g 11.5. |t central limit theorem for the needlets bispectrum -- |g 12. |t Spin Random Fields -- |g 12.1. |t Introduction -- |g 12.2. |t Motivations -- |g 12.3. |t Geometric background -- |g 12.4. |t Spin needlets and spin random fields -- |g 12.5. |t Spin needlets spectral estimator -- |g 12.6. |t Detection of asymmetries -- |g 12.7. |t Estimation with noise -- |g 13. |t Appendix -- |g 13.1. |t Orthogonal polynomials -- |g 13.2. |t Spherical harmonics and their analytic properties -- |g 13.3. |t proof of needlets' localization. |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH13431315 | ||
| 938 | |a Coutts Information Services |b COUT |n 19724677 |c 40.00 GBP | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL775025 | ||
| 938 | |a ebrary |b EBRY |n ebr10502831 | ||
| 938 | |a EBSCOhost |b EBSC |n 399346 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n 329617 | ||
| 938 | |a YBP Library Services |b YANK |n 7166957 | ||
| 938 | |a YBP Library Services |b YANK |n 7205477 | ||
| 938 | |a YBP Library Services |b YANK |n 7302921 | ||
| 938 | |a YBP Library Services |b YANK |n 7319595 | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH28322216 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn769341761 |
|---|---|
| _version_ | 1816881780892893184 |
| adam_text | |
| any_adam_object | |
| author | Marinucci, Domenico |
| author2 | Peccati, Giovanni, 1975- |
| author2_role | |
| author2_variant | g p gp |
| author_GND | http://id.loc.gov/authorities/names/n2011037471 |
| author_facet | Marinucci, Domenico Peccati, Giovanni, 1975- |
| author_role | |
| author_sort | Marinucci, Domenico |
| author_variant | d m dm |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA406 |
| callnumber-raw | QA406 .M37 2011 |
| callnumber-search | QA406 .M37 2011 |
| callnumber-sort | QA 3406 M37 42011 |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Cover; Title; Copyright; Contents; Dedication; Preface; 1 Introduction; 1.1 Overview; 1.2 Cosmological motivations; 1.3 Mathematical framework; 1.4 Plan of the book; 2 Background Results in Representation Theory; 2.1 Introduction; 2.2 Preliminary remarks; 2.3 Groups: basic definitions; 2.3.1 First definitions and examples; 2.3.2 Cosets and quotients; 2.3.3 Actions; 2.4 Representations of compact groups; 2.4.1 Basic definitions; 2.4.2 Group representations and Schur Lemma; 2.4.3 Direct sum and tensor product representations; 2.4.4 Orthogonality relations; 2.5 The Peter-Weyl Theorem. 3 Representations of SO(3) and Harmonic Analysis on S23.1 Introduction; 3.2 Euler angles; 3.2.1 Euler angles for SU(2); 3.2.2 Euler angles for SO(3); 3.3 Wigner's D matrices; 3.3.1 A family of unitary representations of SU(2); 3.3.2 Expressions in terms of Euler angles and irreducibility; 3.3.3 Further properties; 3.3.4 The dual of SO(3); 3.4 Spherical harmonics and Fourier analysis on S2; 3.4.1 Spherical harmonics and Wigner's Dl matrices; 3.4.2 Some properties of spherical harmonics; 3.4.3 An alternative characterization of spherical harmonics; 3.5 The Clebsch-Gordan coefficients. 3.5.1 Clebsch-Gordan matrices3.5.2 Integrals of multiple spherical harmonics; 3.5.3 Wigner 3 j coefficients; 4 Background Results in Probability and Graphical Methods; 4.1 Introduction; 4.2 Brownian motion and stochastic calculus; 4.3 Moments, cumulants and diagram formulae; 4.4 The simplified method of moments on Wiener chaos; 4.4.1 Real kernels; 4.4.2 Further results on complex kernels; 4.5 The graphical method for Wigner coefficients; 4.5.1 From diagrams to graphs; 4.5.2 Further notation; 4.5.3 First example: sums of squares; 4.5.4 Cliques and Wigner 6 j coefficients. 4.5.5 Rule n. 1: loops are zero4.5.6 Rule n. 2: paired sums are one; 4.5.7 Rule n. 3: 2-loops can be cut, and leave a factor; 4.5.8 Rule n. 4: three-loops can be cut, and leave a clique; 5 Spectral Representations; 5.1 Introduction; 5.2 The Stochastic Peter-Weyl Theorem; 5.2.1 General statements; 5.2.2 Decompositions on the sphere; 5.3 Weakly stationary random fields in Rm; 5.4 Stationarity and weak isotropy in R3; 6 Characterizations of Isotropy; 6.1 Introduction; 6.2 First example: the cyclic group; 6.3 The spherical harmonics coefficients; 6.4 Group representations and polyspectra. 6.5 Angular polyspectra and the structure of?l1 ... ln6.5.1 Spectra of strongly isotropic fields; 6.5.2 The structure of?l1 ... ln; 6.6 Reduced polyspectra of arbitrary orders; 6.7 Some examples; 7 Limit Theorems for Gaussian Subordinated Random Fields; 7.1 Introduction; 7.2 First example: the circle; 7.3 Preliminaries on Gaussian-subordinated fields; 7.4 High-frequency CLTs; 7.4.1 Hermite subordination; 7.5 Convolutions and random walks; 7.5.1 Convolutions on?SO (3); 7.5.2 The cases q = 2 and q = 3; 7.5.3 The case of a general q: results and conjectures; 7.6 Further remarks. |
| ctrlnum | (OCoLC)769341761 |
| dewey-full | 523.101/5195 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 523 - Specific celestial bodies and phenomena |
| dewey-raw | 523.101/5195 |
| dewey-search | 523.101/5195 |
| dewey-sort | 3523.101 45195 |
| dewey-tens | 520 - Astronomy and allied sciences |
| discipline | Physik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>10313cam a2200949Mi 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn769341761</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr |n|---|||||</controlfield><controlfield tag="008">111226s2011 enk ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">EBLCP</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">EBLCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">IDEBK</subfield><subfield code="d">OL$</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">CDX</subfield><subfield code="d">OCLCF</subfield><subfield code="d">N$T</subfield><subfield code="d">E7B</subfield><subfield code="d">YDXCP</subfield><subfield code="d">UIU</subfield><subfield code="d">REDDC</subfield><subfield code="d">CAMBR</subfield><subfield code="d">OSU</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UAB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">INT</subfield><subfield code="d">AU@</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield></datafield><datafield tag="066" ind1=" " ind2=" "><subfield code="c">(S</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">759007197</subfield><subfield code="a">761284104</subfield><subfield code="a">768771958</subfield><subfield code="a">816866945</subfield><subfield code="a">819630810</subfield><subfield code="a">853654206</subfield><subfield code="a">1178961534</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139117487</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139117483</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1283296179</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781283296175</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511751677</subfield><subfield code="q">(electronic book)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0511751672</subfield><subfield code="q">(electronic book)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139128148</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139128140</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139115316</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139115315</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">0521175615</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9780521175616</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139113120</subfield><subfield code="q">(e-book)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139113127</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)769341761</subfield><subfield code="z">(OCoLC)759007197</subfield><subfield code="z">(OCoLC)761284104</subfield><subfield code="z">(OCoLC)768771958</subfield><subfield code="z">(OCoLC)816866945</subfield><subfield code="z">(OCoLC)819630810</subfield><subfield code="z">(OCoLC)853654206</subfield><subfield code="z">(OCoLC)1178961534</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA406 .M37 2011</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">PBT</subfield><subfield code="2">bicssc</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">SCI</subfield><subfield code="x">015000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">523.101/5195</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT029000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Marinucci, Domenico.</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Random Fields on the Sphere :</subfield><subfield code="b">Representation, Limit Theorems and Cosmological Applications.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Cambridge :</subfield><subfield code="b">Cambridge University Press,</subfield><subfield code="c">2011.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (355 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">London Mathematical Society Lecture Note Series, 389 ;</subfield><subfield code="v">v. 389</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="6">880-01</subfield><subfield code="a">Cover; Title; Copyright; Contents; Dedication; Preface; 1 Introduction; 1.1 Overview; 1.2 Cosmological motivations; 1.3 Mathematical framework; 1.4 Plan of the book; 2 Background Results in Representation Theory; 2.1 Introduction; 2.2 Preliminary remarks; 2.3 Groups: basic definitions; 2.3.1 First definitions and examples; 2.3.2 Cosets and quotients; 2.3.3 Actions; 2.4 Representations of compact groups; 2.4.1 Basic definitions; 2.4.2 Group representations and Schur Lemma; 2.4.3 Direct sum and tensor product representations; 2.4.4 Orthogonality relations; 2.5 The Peter-Weyl Theorem.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3 Representations of SO(3) and Harmonic Analysis on S23.1 Introduction; 3.2 Euler angles; 3.2.1 Euler angles for SU(2); 3.2.2 Euler angles for SO(3); 3.3 Wigner's D matrices; 3.3.1 A family of unitary representations of SU(2); 3.3.2 Expressions in terms of Euler angles and irreducibility; 3.3.3 Further properties; 3.3.4 The dual of SO(3); 3.4 Spherical harmonics and Fourier analysis on S2; 3.4.1 Spherical harmonics and Wigner's Dl matrices; 3.4.2 Some properties of spherical harmonics; 3.4.3 An alternative characterization of spherical harmonics; 3.5 The Clebsch-Gordan coefficients.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3.5.1 Clebsch-Gordan matrices3.5.2 Integrals of multiple spherical harmonics; 3.5.3 Wigner 3 j coefficients; 4 Background Results in Probability and Graphical Methods; 4.1 Introduction; 4.2 Brownian motion and stochastic calculus; 4.3 Moments, cumulants and diagram formulae; 4.4 The simplified method of moments on Wiener chaos; 4.4.1 Real kernels; 4.4.2 Further results on complex kernels; 4.5 The graphical method for Wigner coefficients; 4.5.1 From diagrams to graphs; 4.5.2 Further notation; 4.5.3 First example: sums of squares; 4.5.4 Cliques and Wigner 6 j coefficients.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">4.5.5 Rule n. 1: loops are zero4.5.6 Rule n. 2: paired sums are one; 4.5.7 Rule n. 3: 2-loops can be cut, and leave a factor; 4.5.8 Rule n. 4: three-loops can be cut, and leave a clique; 5 Spectral Representations; 5.1 Introduction; 5.2 The Stochastic Peter-Weyl Theorem; 5.2.1 General statements; 5.2.2 Decompositions on the sphere; 5.3 Weakly stationary random fields in Rm; 5.4 Stationarity and weak isotropy in R3; 6 Characterizations of Isotropy; 6.1 Introduction; 6.2 First example: the cyclic group; 6.3 The spherical harmonics coefficients; 6.4 Group representations and polyspectra.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">6.5 Angular polyspectra and the structure of?l1 ... ln6.5.1 Spectra of strongly isotropic fields; 6.5.2 The structure of?l1 ... ln; 6.6 Reduced polyspectra of arbitrary orders; 6.7 Some examples; 7 Limit Theorems for Gaussian Subordinated Random Fields; 7.1 Introduction; 7.2 First example: the circle; 7.3 Preliminaries on Gaussian-subordinated fields; 7.4 High-frequency CLTs; 7.4.1 Hermite subordination; 7.5 Convolutions and random walks; 7.5.1 Convolutions on?SO (3); 7.5.2 The cases q = 2 and q = 3; 7.5.3 The case of a general q: results and conjectures; 7.6 Further remarks.</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">7.6.1 Convolutions as mixed states.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Reviews recent developments in the analysis of isotropic spherical random fields, with a view towards applications in cosmology.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 326-337) and index.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Compact groups.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85029280</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Cosmology</subfield><subfield code="x">Statistical methods.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Random fields.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85111347</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Spherical harmonics.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85126596</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Groupes compacts.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Cosmologie</subfield><subfield code="x">Méthodes statistiques.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Champs aléatoires.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Harmoniques sphériques.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Probability & Statistics</subfield><subfield code="x">General.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE</subfield><subfield code="x">Cosmology.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Compact groups</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Random fields</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Spherical harmonics</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Peccati, Giovanni,</subfield><subfield code="d">1975-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjHW3xR6VdxggCgh4BRBT3</subfield><subfield code="0">http://id.loc.gov/authorities/names/n2011037471</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Marinucci, Domenico.</subfield><subfield code="t">Random Fields on the Sphere : Representation, Limit Theorems and Cosmological Applications.</subfield><subfield code="d">Cambridge : Cambridge University Press, ©2011</subfield><subfield code="z">9780521175616</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">London Mathematical Society Lecture Note Series, 389.</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=399346</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="880" ind1="0" ind2="0"><subfield code="6">505-01/(S</subfield><subfield code="g">Machine generated contents note:</subfield><subfield code="g">1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">1.1.</subfield><subfield code="t">Overview --</subfield><subfield code="g">1.2.</subfield><subfield code="t">Cosmological motivations --</subfield><subfield code="g">1.3.</subfield><subfield code="t">Mathematical framework --</subfield><subfield code="g">1.4.</subfield><subfield code="t">Plan of the book --</subfield><subfield code="g">2.</subfield><subfield code="t">Background Results in Representation Theory --</subfield><subfield code="g">2.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">2.2.</subfield><subfield code="t">Preliminary remarks --</subfield><subfield code="g">2.3.</subfield><subfield code="t">Groups: basic definitions --</subfield><subfield code="g">2.4.</subfield><subfield code="t">Representations of compact groups --</subfield><subfield code="g">2.5.</subfield><subfield code="t">Peter-Weyl Theorem --</subfield><subfield code="g">3.</subfield><subfield code="t">Representations of SO(3) and Harmonic Analysis on S2 --</subfield><subfield code="g">3.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">3.2.</subfield><subfield code="t">Euler angles --</subfield><subfield code="g">3.3.</subfield><subfield code="t">Wigner's D matrices --</subfield><subfield code="g">3.4.</subfield><subfield code="t">Spherical harmonics and Fourier analysis on S2 --</subfield><subfield code="g">3.5.</subfield><subfield code="t">Clebsch-Gordan coefficients --</subfield><subfield code="g">4.</subfield><subfield code="t">Background Results in Probability and Graphical Methods --</subfield><subfield code="g">4.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">4.2.</subfield><subfield code="t">Brownian motion and stochastic calculus --</subfield><subfield code="g">4.3.</subfield><subfield code="t">Moments, cumulants and diagram formulae --</subfield><subfield code="g">4.4.</subfield><subfield code="t">simplified method of moments on Wiener chaos --</subfield><subfield code="g">4.5.</subfield><subfield code="t">graphical method for Wigner coefficients --</subfield><subfield code="g">5.</subfield><subfield code="t">Spectral Representations --</subfield><subfield code="g">5.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">5.2.</subfield><subfield code="t">Stochastic Peter-Weyl Theorem --</subfield><subfield code="g">5.3.</subfield><subfield code="t">Weakly stationary random fields in Rm --</subfield><subfield code="g">5.4.</subfield><subfield code="t">Stationarity and weak isotropy in R3 --</subfield><subfield code="g">6.</subfield><subfield code="t">Characterizations of Isotropy --</subfield><subfield code="g">6.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">6.2.</subfield><subfield code="t">First example: the cyclic group --</subfield><subfield code="g">6.3.</subfield><subfield code="t">spherical harmonics coefficients --</subfield><subfield code="g">6.4.</subfield><subfield code="t">Group representations and polyspectra --</subfield><subfield code="g">6.5.</subfield><subfield code="t">Angular polyspectra and the structure of δl1 ... l1 --</subfield><subfield code="g">6.6.</subfield><subfield code="t">Reduced polyspectra of arbitrary orders --</subfield><subfield code="g">6.7.</subfield><subfield code="t">Some examples --</subfield><subfield code="g">7.</subfield><subfield code="t">Limit Theorems for Gaussian Subordinated Random Fields --</subfield><subfield code="g">7.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">7.2.</subfield><subfield code="t">First example: the circle --</subfield><subfield code="g">7.3.</subfield><subfield code="t">Preliminaries on Gaussian-subordinated fields --</subfield><subfield code="g">7.4.</subfield><subfield code="t">High-frequency CLTs --</subfield><subfield code="g">7.5.</subfield><subfield code="t">Convolutions and random walks --</subfield><subfield code="g">7.6.</subfield><subfield code="t">Further remarks --</subfield><subfield code="g">7.7.</subfield><subfield code="t">Application: algebraic/exponential dualities --</subfield><subfield code="g">8.</subfield><subfield code="t">Asymptotics for the Sample Power Spectrum --</subfield><subfield code="g">8.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">8.2.</subfield><subfield code="t">Angular power spectrum estimation --</subfield><subfield code="g">8.3.</subfield><subfield code="t">Interlude: some practical issues --</subfield><subfield code="g">8.4.</subfield><subfield code="t">Asymptotics in the non-Gaussian case --</subfield><subfield code="g">8.5.</subfield><subfield code="t">quadratic case --</subfield><subfield code="g">8.6.</subfield><subfield code="t">Discussion --</subfield><subfield code="g">9.</subfield><subfield code="t">Asymptotics for Sample Bispectra --</subfield><subfield code="g">9.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">9.2.</subfield><subfield code="t">Sample bispectra --</subfield><subfield code="g">9.3.</subfield><subfield code="t">central limit theorem --</subfield><subfield code="g">9.4.</subfield><subfield code="t">Limit theorems under random normalizations --</subfield><subfield code="g">9.5.</subfield><subfield code="t">Testing for non-Gaussianity --</subfield><subfield code="g">10.</subfield><subfield code="t">Spherical Needlets and their Asymptotic Properties --</subfield><subfield code="g">10.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">10.2.</subfield><subfield code="t">construction of spherical needlets --</subfield><subfield code="g">10.3.</subfield><subfield code="t">Properties of spherical needlets --</subfield><subfield code="g">10.4.</subfield><subfield code="t">Stochastic properties of needlet coefficients --</subfield><subfield code="g">10.5.</subfield><subfield code="t">Missing observations --</subfield><subfield code="g">10.6.</subfield><subfield code="t">Mexican needlets --</subfield><subfield code="g">11.</subfield><subfield code="t">Needlets Estimation of Power Spectrum and Bispectrum --</subfield><subfield code="g">11.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">11.2.</subfield><subfield code="t">general convergence result --</subfield><subfield code="g">11.3.</subfield><subfield code="t">Estimation of the angular power spectrum --</subfield><subfield code="g">11.4.</subfield><subfield code="t">functional central limit theorem --</subfield><subfield code="g">11.5.</subfield><subfield code="t">central limit theorem for the needlets bispectrum --</subfield><subfield code="g">12.</subfield><subfield code="t">Spin Random Fields --</subfield><subfield code="g">12.1.</subfield><subfield code="t">Introduction --</subfield><subfield code="g">12.2.</subfield><subfield code="t">Motivations --</subfield><subfield code="g">12.3.</subfield><subfield code="t">Geometric background --</subfield><subfield code="g">12.4.</subfield><subfield code="t">Spin needlets and spin random fields --</subfield><subfield code="g">12.5.</subfield><subfield code="t">Spin needlets spectral estimator --</subfield><subfield code="g">12.6.</subfield><subfield code="t">Detection of asymmetries --</subfield><subfield code="g">12.7.</subfield><subfield code="t">Estimation with noise --</subfield><subfield code="g">13.</subfield><subfield code="t">Appendix --</subfield><subfield code="g">13.1.</subfield><subfield code="t">Orthogonal polynomials --</subfield><subfield code="g">13.2.</subfield><subfield code="t">Spherical harmonics and their analytic properties --</subfield><subfield code="g">13.3.</subfield><subfield code="t">proof of needlets' localization.</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH13431315</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Coutts Information Services</subfield><subfield code="b">COUT</subfield><subfield code="n">19724677</subfield><subfield code="c">40.00 GBP</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBL - Ebook Library</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL775025</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10502831</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">399346</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">329617</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7166957</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7205477</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7302921</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7319595</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH28322216</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn769341761 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:10Z |
| institution | BVB |
| isbn | 9781139117487 1139117483 1283296179 9781283296175 9780511751677 0511751672 9781139128148 1139128140 1139115316 9781139115315 9781139113120 1139113127 |
| language | English |
| oclc_num | 769341761 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (355 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society Lecture Note Series, 389. |
| series2 | London Mathematical Society Lecture Note Series, 389 ; |
| spelling | Marinucci, Domenico. Random Fields on the Sphere : Representation, Limit Theorems and Cosmological Applications. Cambridge : Cambridge University Press, 2011. 1 online resource (355 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society Lecture Note Series, 389 ; v. 389 880-01 Cover; Title; Copyright; Contents; Dedication; Preface; 1 Introduction; 1.1 Overview; 1.2 Cosmological motivations; 1.3 Mathematical framework; 1.4 Plan of the book; 2 Background Results in Representation Theory; 2.1 Introduction; 2.2 Preliminary remarks; 2.3 Groups: basic definitions; 2.3.1 First definitions and examples; 2.3.2 Cosets and quotients; 2.3.3 Actions; 2.4 Representations of compact groups; 2.4.1 Basic definitions; 2.4.2 Group representations and Schur Lemma; 2.4.3 Direct sum and tensor product representations; 2.4.4 Orthogonality relations; 2.5 The Peter-Weyl Theorem. 3 Representations of SO(3) and Harmonic Analysis on S23.1 Introduction; 3.2 Euler angles; 3.2.1 Euler angles for SU(2); 3.2.2 Euler angles for SO(3); 3.3 Wigner's D matrices; 3.3.1 A family of unitary representations of SU(2); 3.3.2 Expressions in terms of Euler angles and irreducibility; 3.3.3 Further properties; 3.3.4 The dual of SO(3); 3.4 Spherical harmonics and Fourier analysis on S2; 3.4.1 Spherical harmonics and Wigner's Dl matrices; 3.4.2 Some properties of spherical harmonics; 3.4.3 An alternative characterization of spherical harmonics; 3.5 The Clebsch-Gordan coefficients. 3.5.1 Clebsch-Gordan matrices3.5.2 Integrals of multiple spherical harmonics; 3.5.3 Wigner 3 j coefficients; 4 Background Results in Probability and Graphical Methods; 4.1 Introduction; 4.2 Brownian motion and stochastic calculus; 4.3 Moments, cumulants and diagram formulae; 4.4 The simplified method of moments on Wiener chaos; 4.4.1 Real kernels; 4.4.2 Further results on complex kernels; 4.5 The graphical method for Wigner coefficients; 4.5.1 From diagrams to graphs; 4.5.2 Further notation; 4.5.3 First example: sums of squares; 4.5.4 Cliques and Wigner 6 j coefficients. 4.5.5 Rule n. 1: loops are zero4.5.6 Rule n. 2: paired sums are one; 4.5.7 Rule n. 3: 2-loops can be cut, and leave a factor; 4.5.8 Rule n. 4: three-loops can be cut, and leave a clique; 5 Spectral Representations; 5.1 Introduction; 5.2 The Stochastic Peter-Weyl Theorem; 5.2.1 General statements; 5.2.2 Decompositions on the sphere; 5.3 Weakly stationary random fields in Rm; 5.4 Stationarity and weak isotropy in R3; 6 Characterizations of Isotropy; 6.1 Introduction; 6.2 First example: the cyclic group; 6.3 The spherical harmonics coefficients; 6.4 Group representations and polyspectra. 6.5 Angular polyspectra and the structure of?l1 ... ln6.5.1 Spectra of strongly isotropic fields; 6.5.2 The structure of?l1 ... ln; 6.6 Reduced polyspectra of arbitrary orders; 6.7 Some examples; 7 Limit Theorems for Gaussian Subordinated Random Fields; 7.1 Introduction; 7.2 First example: the circle; 7.3 Preliminaries on Gaussian-subordinated fields; 7.4 High-frequency CLTs; 7.4.1 Hermite subordination; 7.5 Convolutions and random walks; 7.5.1 Convolutions on?SO (3); 7.5.2 The cases q = 2 and q = 3; 7.5.3 The case of a general q: results and conjectures; 7.6 Further remarks. 7.6.1 Convolutions as mixed states. Reviews recent developments in the analysis of isotropic spherical random fields, with a view towards applications in cosmology. Print version record. Includes bibliographical references (pages 326-337) and index. Compact groups. http://id.loc.gov/authorities/subjects/sh85029280 Cosmology Statistical methods. Random fields. http://id.loc.gov/authorities/subjects/sh85111347 Spherical harmonics. http://id.loc.gov/authorities/subjects/sh85126596 Groupes compacts. Cosmologie Méthodes statistiques. Champs aléatoires. Harmoniques sphériques. MATHEMATICS Probability & Statistics General. bisacsh SCIENCE Cosmology. bisacsh Compact groups fast Random fields fast Spherical harmonics fast Peccati, Giovanni, 1975- https://id.oclc.org/worldcat/entity/E39PCjHW3xR6VdxggCgh4BRBT3 http://id.loc.gov/authorities/names/n2011037471 Print version: Marinucci, Domenico. Random Fields on the Sphere : Representation, Limit Theorems and Cosmological Applications. Cambridge : Cambridge University Press, ©2011 9780521175616 London Mathematical Society Lecture Note Series, 389. FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=399346 Volltext 505-01/(S Machine generated contents note: 1. Introduction -- 1.1. Overview -- 1.2. Cosmological motivations -- 1.3. Mathematical framework -- 1.4. Plan of the book -- 2. Background Results in Representation Theory -- 2.1. Introduction -- 2.2. Preliminary remarks -- 2.3. Groups: basic definitions -- 2.4. Representations of compact groups -- 2.5. Peter-Weyl Theorem -- 3. Representations of SO(3) and Harmonic Analysis on S2 -- 3.1. Introduction -- 3.2. Euler angles -- 3.3. Wigner's D matrices -- 3.4. Spherical harmonics and Fourier analysis on S2 -- 3.5. Clebsch-Gordan coefficients -- 4. Background Results in Probability and Graphical Methods -- 4.1. Introduction -- 4.2. Brownian motion and stochastic calculus -- 4.3. Moments, cumulants and diagram formulae -- 4.4. simplified method of moments on Wiener chaos -- 4.5. graphical method for Wigner coefficients -- 5. Spectral Representations -- 5.1. Introduction -- 5.2. Stochastic Peter-Weyl Theorem -- 5.3. Weakly stationary random fields in Rm -- 5.4. Stationarity and weak isotropy in R3 -- 6. Characterizations of Isotropy -- 6.1. Introduction -- 6.2. First example: the cyclic group -- 6.3. spherical harmonics coefficients -- 6.4. Group representations and polyspectra -- 6.5. Angular polyspectra and the structure of δl1 ... l1 -- 6.6. Reduced polyspectra of arbitrary orders -- 6.7. Some examples -- 7. Limit Theorems for Gaussian Subordinated Random Fields -- 7.1. Introduction -- 7.2. First example: the circle -- 7.3. Preliminaries on Gaussian-subordinated fields -- 7.4. High-frequency CLTs -- 7.5. Convolutions and random walks -- 7.6. Further remarks -- 7.7. Application: algebraic/exponential dualities -- 8. Asymptotics for the Sample Power Spectrum -- 8.1. Introduction -- 8.2. Angular power spectrum estimation -- 8.3. Interlude: some practical issues -- 8.4. Asymptotics in the non-Gaussian case -- 8.5. quadratic case -- 8.6. Discussion -- 9. Asymptotics for Sample Bispectra -- 9.1. Introduction -- 9.2. Sample bispectra -- 9.3. central limit theorem -- 9.4. Limit theorems under random normalizations -- 9.5. Testing for non-Gaussianity -- 10. Spherical Needlets and their Asymptotic Properties -- 10.1. Introduction -- 10.2. construction of spherical needlets -- 10.3. Properties of spherical needlets -- 10.4. Stochastic properties of needlet coefficients -- 10.5. Missing observations -- 10.6. Mexican needlets -- 11. Needlets Estimation of Power Spectrum and Bispectrum -- 11.1. Introduction -- 11.2. general convergence result -- 11.3. Estimation of the angular power spectrum -- 11.4. functional central limit theorem -- 11.5. central limit theorem for the needlets bispectrum -- 12. Spin Random Fields -- 12.1. Introduction -- 12.2. Motivations -- 12.3. Geometric background -- 12.4. Spin needlets and spin random fields -- 12.5. Spin needlets spectral estimator -- 12.6. Detection of asymmetries -- 12.7. Estimation with noise -- 13. Appendix -- 13.1. Orthogonal polynomials -- 13.2. Spherical harmonics and their analytic properties -- 13.3. proof of needlets' localization. |
| spellingShingle | Marinucci, Domenico Random Fields on the Sphere : Representation, Limit Theorems and Cosmological Applications. London Mathematical Society Lecture Note Series, 389. Cover; Title; Copyright; Contents; Dedication; Preface; 1 Introduction; 1.1 Overview; 1.2 Cosmological motivations; 1.3 Mathematical framework; 1.4 Plan of the book; 2 Background Results in Representation Theory; 2.1 Introduction; 2.2 Preliminary remarks; 2.3 Groups: basic definitions; 2.3.1 First definitions and examples; 2.3.2 Cosets and quotients; 2.3.3 Actions; 2.4 Representations of compact groups; 2.4.1 Basic definitions; 2.4.2 Group representations and Schur Lemma; 2.4.3 Direct sum and tensor product representations; 2.4.4 Orthogonality relations; 2.5 The Peter-Weyl Theorem. 3 Representations of SO(3) and Harmonic Analysis on S23.1 Introduction; 3.2 Euler angles; 3.2.1 Euler angles for SU(2); 3.2.2 Euler angles for SO(3); 3.3 Wigner's D matrices; 3.3.1 A family of unitary representations of SU(2); 3.3.2 Expressions in terms of Euler angles and irreducibility; 3.3.3 Further properties; 3.3.4 The dual of SO(3); 3.4 Spherical harmonics and Fourier analysis on S2; 3.4.1 Spherical harmonics and Wigner's Dl matrices; 3.4.2 Some properties of spherical harmonics; 3.4.3 An alternative characterization of spherical harmonics; 3.5 The Clebsch-Gordan coefficients. 3.5.1 Clebsch-Gordan matrices3.5.2 Integrals of multiple spherical harmonics; 3.5.3 Wigner 3 j coefficients; 4 Background Results in Probability and Graphical Methods; 4.1 Introduction; 4.2 Brownian motion and stochastic calculus; 4.3 Moments, cumulants and diagram formulae; 4.4 The simplified method of moments on Wiener chaos; 4.4.1 Real kernels; 4.4.2 Further results on complex kernels; 4.5 The graphical method for Wigner coefficients; 4.5.1 From diagrams to graphs; 4.5.2 Further notation; 4.5.3 First example: sums of squares; 4.5.4 Cliques and Wigner 6 j coefficients. 4.5.5 Rule n. 1: loops are zero4.5.6 Rule n. 2: paired sums are one; 4.5.7 Rule n. 3: 2-loops can be cut, and leave a factor; 4.5.8 Rule n. 4: three-loops can be cut, and leave a clique; 5 Spectral Representations; 5.1 Introduction; 5.2 The Stochastic Peter-Weyl Theorem; 5.2.1 General statements; 5.2.2 Decompositions on the sphere; 5.3 Weakly stationary random fields in Rm; 5.4 Stationarity and weak isotropy in R3; 6 Characterizations of Isotropy; 6.1 Introduction; 6.2 First example: the cyclic group; 6.3 The spherical harmonics coefficients; 6.4 Group representations and polyspectra. 6.5 Angular polyspectra and the structure of?l1 ... ln6.5.1 Spectra of strongly isotropic fields; 6.5.2 The structure of?l1 ... ln; 6.6 Reduced polyspectra of arbitrary orders; 6.7 Some examples; 7 Limit Theorems for Gaussian Subordinated Random Fields; 7.1 Introduction; 7.2 First example: the circle; 7.3 Preliminaries on Gaussian-subordinated fields; 7.4 High-frequency CLTs; 7.4.1 Hermite subordination; 7.5 Convolutions and random walks; 7.5.1 Convolutions on?SO (3); 7.5.2 The cases q = 2 and q = 3; 7.5.3 The case of a general q: results and conjectures; 7.6 Further remarks. Compact groups. http://id.loc.gov/authorities/subjects/sh85029280 Cosmology Statistical methods. Random fields. http://id.loc.gov/authorities/subjects/sh85111347 Spherical harmonics. http://id.loc.gov/authorities/subjects/sh85126596 Groupes compacts. Cosmologie Méthodes statistiques. Champs aléatoires. Harmoniques sphériques. MATHEMATICS Probability & Statistics General. bisacsh SCIENCE Cosmology. bisacsh Compact groups fast Random fields fast Spherical harmonics fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85029280 http://id.loc.gov/authorities/subjects/sh85111347 http://id.loc.gov/authorities/subjects/sh85126596 |
| title | Random Fields on the Sphere : Representation, Limit Theorems and Cosmological Applications. |
| title_auth | Random Fields on the Sphere : Representation, Limit Theorems and Cosmological Applications. |
| title_exact_search | Random Fields on the Sphere : Representation, Limit Theorems and Cosmological Applications. |
| title_full | Random Fields on the Sphere : Representation, Limit Theorems and Cosmological Applications. |
| title_fullStr | Random Fields on the Sphere : Representation, Limit Theorems and Cosmological Applications. |
| title_full_unstemmed | Random Fields on the Sphere : Representation, Limit Theorems and Cosmological Applications. |
| title_short | Random Fields on the Sphere : |
| title_sort | random fields on the sphere representation limit theorems and cosmological applications |
| title_sub | Representation, Limit Theorems and Cosmological Applications. |
| topic | Compact groups. http://id.loc.gov/authorities/subjects/sh85029280 Cosmology Statistical methods. Random fields. http://id.loc.gov/authorities/subjects/sh85111347 Spherical harmonics. http://id.loc.gov/authorities/subjects/sh85126596 Groupes compacts. Cosmologie Méthodes statistiques. Champs aléatoires. Harmoniques sphériques. MATHEMATICS Probability & Statistics General. bisacsh SCIENCE Cosmology. bisacsh Compact groups fast Random fields fast Spherical harmonics fast |
| topic_facet | Compact groups. Cosmology Statistical methods. Random fields. Spherical harmonics. Groupes compacts. Cosmologie Méthodes statistiques. Champs aléatoires. Harmoniques sphériques. MATHEMATICS Probability & Statistics General. SCIENCE Cosmology. Compact groups Random fields Spherical harmonics |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=399346 |
| work_keys_str_mv | AT marinuccidomenico randomfieldsonthesphererepresentationlimittheoremsandcosmologicalapplications AT peccatigiovanni randomfieldsonthesphererepresentationlimittheoremsandcosmologicalapplications |