Random matrices: high dimensional phenomena
This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups...
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Cambridge
Cambridge University Press
2009
|
Schriftenreihe: | London Mathematical Society lecture note series
367 |
Schlagworte: | |
Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
Zusammenfassung: | This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium |
Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
Beschreibung: | 1 online resource (x, 437 pages) |
ISBN: | 9781139107129 |
DOI: | 10.1017/CBO9781139107129 |
Internformat
MARC
LEADER | 00000nmm a2200000zcb4500 | ||
---|---|---|---|
001 | BV043941785 | ||
003 | DE-604 | ||
005 | 00000000000000.0 | ||
007 | cr|uuu---uuuuu | ||
008 | 161206s2009 |||| o||u| ||||||eng d | ||
020 | |a 9781139107129 |c Online |9 978-1-139-10712-9 | ||
024 | 7 | |a 10.1017/CBO9781139107129 |2 doi | |
035 | |a (ZDB-20-CBO)CR9781139107129 | ||
035 | |a (OCoLC)859643412 | ||
035 | |a (DE-599)BVBBV043941785 | ||
040 | |a DE-604 |b ger |e rda | ||
041 | 0 | |a eng | |
049 | |a DE-12 |a DE-92 | ||
082 | 0 | |a 512.9434 |2 22 | |
084 | |a SI 320 |0 (DE-625)143123: |2 rvk | ||
084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
100 | 1 | |a Blower, G. |e Verfasser |4 aut | |
245 | 1 | 0 | |a Random matrices |b high dimensional phenomena |c Gordon Blower |
264 | 1 | |a Cambridge |b Cambridge University Press |c 2009 | |
300 | |a 1 online resource (x, 437 pages) | ||
336 | |b txt |2 rdacontent | ||
337 | |b c |2 rdamedia | ||
338 | |b cr |2 rdacarrier | ||
490 | 0 | |a London Mathematical Society lecture note series |v 367 | |
500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
505 | 8 | |a Metric measure spaces -- Lie groups and matrix ensembles -- Entropy and concentration of measure -- Free entropy and equilibrium -- Convergence to equilibrium -- Gradient flows and functional inequalities -- Young tableaux -- Random point fields and random matrices -- Integrable operators and differential equations -- Fluctuations and the Tracy-Widom distribution -- Limit groups and Gaussian measures -- Hermite polynomials -- From the Ornstein-Uhlenbeck process to the Burgers equation -- Noncommutative probability spaces | |
520 | |a This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium | ||
650 | 4 | |a Random matrices | |
650 | 0 | 7 | |a Stochastische Matrix |0 (DE-588)4057624-3 |2 gnd |9 rswk-swf |
689 | 0 | 0 | |a Stochastische Matrix |0 (DE-588)4057624-3 |D s |
689 | 0 | |8 1\p |5 DE-604 | |
776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-13312-8 |
856 | 4 | 0 | |u https://doi.org/10.1017/CBO9781139107129 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
912 | |a ZDB-20-CBO | ||
999 | |a oai:aleph.bib-bvb.de:BVB01-029350755 | ||
883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
966 | e | |u https://doi.org/10.1017/CBO9781139107129 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
966 | e | |u https://doi.org/10.1017/CBO9781139107129 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext |
Datensatz im Suchindex
_version_ | 1804176883950026753 |
---|---|
any_adam_object | |
author | Blower, G. |
author_facet | Blower, G. |
author_role | aut |
author_sort | Blower, G. |
author_variant | g b gb |
building | Verbundindex |
bvnumber | BV043941785 |
classification_rvk | SI 320 SK 820 |
collection | ZDB-20-CBO |
contents | Metric measure spaces -- Lie groups and matrix ensembles -- Entropy and concentration of measure -- Free entropy and equilibrium -- Convergence to equilibrium -- Gradient flows and functional inequalities -- Young tableaux -- Random point fields and random matrices -- Integrable operators and differential equations -- Fluctuations and the Tracy-Widom distribution -- Limit groups and Gaussian measures -- Hermite polynomials -- From the Ornstein-Uhlenbeck process to the Burgers equation -- Noncommutative probability spaces |
ctrlnum | (ZDB-20-CBO)CR9781139107129 (OCoLC)859643412 (DE-599)BVBBV043941785 |
dewey-full | 512.9434 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 512 - Algebra |
dewey-raw | 512.9434 |
dewey-search | 512.9434 |
dewey-sort | 3512.9434 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
doi_str_mv | 10.1017/CBO9781139107129 |
format | Electronic eBook |
fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03442nmm a2200481zcb4500</leader><controlfield tag="001">BV043941785</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2009 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139107129</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-139-10712-9</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9781139107129</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9781139107129</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)859643412</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043941785</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.9434</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 320</subfield><subfield code="0">(DE-625)143123:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="0">(DE-625)143258:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Blower, G.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Random matrices</subfield><subfield code="b">high dimensional phenomena</subfield><subfield code="c">Gordon Blower</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (x, 437 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">London Mathematical Society lecture note series</subfield><subfield code="v">367</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Oct 2015)</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Metric measure spaces -- Lie groups and matrix ensembles -- Entropy and concentration of measure -- Free entropy and equilibrium -- Convergence to equilibrium -- Gradient flows and functional inequalities -- Young tableaux -- Random point fields and random matrices -- Integrable operators and differential equations -- Fluctuations and the Tracy-Widom distribution -- Limit groups and Gaussian measures -- Hermite polynomials -- From the Ornstein-Uhlenbeck process to the Burgers equation -- Noncommutative probability spaces</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Random matrices</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastische Matrix</subfield><subfield code="0">(DE-588)4057624-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Stochastische Matrix</subfield><subfield code="0">(DE-588)4057624-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-13312-8</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9781139107129</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029350755</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9781139107129</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9781139107129</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
id | DE-604.BV043941785 |
illustrated | Not Illustrated |
indexdate | 2024-07-10T07:39:16Z |
institution | BVB |
isbn | 9781139107129 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350755 |
oclc_num | 859643412 |
open_access_boolean | |
owner | DE-12 DE-92 |
owner_facet | DE-12 DE-92 |
physical | 1 online resource (x, 437 pages) |
psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
publishDate | 2009 |
publishDateSearch | 2009 |
publishDateSort | 2009 |
publisher | Cambridge University Press |
record_format | marc |
series2 | London Mathematical Society lecture note series |
spelling | Blower, G. Verfasser aut Random matrices high dimensional phenomena Gordon Blower Cambridge Cambridge University Press 2009 1 online resource (x, 437 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 367 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Metric measure spaces -- Lie groups and matrix ensembles -- Entropy and concentration of measure -- Free entropy and equilibrium -- Convergence to equilibrium -- Gradient flows and functional inequalities -- Young tableaux -- Random point fields and random matrices -- Integrable operators and differential equations -- Fluctuations and the Tracy-Widom distribution -- Limit groups and Gaussian measures -- Hermite polynomials -- From the Ornstein-Uhlenbeck process to the Burgers equation -- Noncommutative probability spaces This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium Random matrices Stochastische Matrix (DE-588)4057624-3 gnd rswk-swf Stochastische Matrix (DE-588)4057624-3 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-13312-8 https://doi.org/10.1017/CBO9781139107129 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Blower, G. Random matrices high dimensional phenomena Metric measure spaces -- Lie groups and matrix ensembles -- Entropy and concentration of measure -- Free entropy and equilibrium -- Convergence to equilibrium -- Gradient flows and functional inequalities -- Young tableaux -- Random point fields and random matrices -- Integrable operators and differential equations -- Fluctuations and the Tracy-Widom distribution -- Limit groups and Gaussian measures -- Hermite polynomials -- From the Ornstein-Uhlenbeck process to the Burgers equation -- Noncommutative probability spaces Random matrices Stochastische Matrix (DE-588)4057624-3 gnd |
subject_GND | (DE-588)4057624-3 |
title | Random matrices high dimensional phenomena |
title_auth | Random matrices high dimensional phenomena |
title_exact_search | Random matrices high dimensional phenomena |
title_full | Random matrices high dimensional phenomena Gordon Blower |
title_fullStr | Random matrices high dimensional phenomena Gordon Blower |
title_full_unstemmed | Random matrices high dimensional phenomena Gordon Blower |
title_short | Random matrices |
title_sort | random matrices high dimensional phenomena |
title_sub | high dimensional phenomena |
topic | Random matrices Stochastische Matrix (DE-588)4057624-3 gnd |
topic_facet | Random matrices Stochastische Matrix |
url | https://doi.org/10.1017/CBO9781139107129 |
work_keys_str_mv | AT blowerg randommatriceshighdimensionalphenomena |