Noise sensitivity of boolean functions and percolation:
This is a graduate-level introduction to the theory of Boolean functions, an exciting area lying on the border of probability theory, discrete mathematics, analysis, and theoretical computer science. Certain functions are highly sensitive to noise; this can be seen via Fourier analysis on the hyperc...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2015
|
| Schriftenreihe: | Institute of Mathematical Statistics textbooks
5 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | This is a graduate-level introduction to the theory of Boolean functions, an exciting area lying on the border of probability theory, discrete mathematics, analysis, and theoretical computer science. Certain functions are highly sensitive to noise; this can be seen via Fourier analysis on the hypercube. The key model analyzed in depth is critical percolation on the hexagonal lattice. For this model, the critical exponents, previously determined using the now-famous Schramm–Loewner evolution, appear here in the study of sensitivity behavior. Even for this relatively simple model, beyond the Fourier-analytic set-up, there are three crucially important but distinct approaches: hypercontractivity of operators, connections to randomized algorithms, and viewing the spectrum as a random Cantor set. This book assumes a basic background in probability theory and integration theory. Each chapter ends with exercises, some straightforward, some challenging |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xvii, 203 pages) |
| ISBN: | 9781139924160 |
| DOI: | 10.1017/CBO9781139924160 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043940245 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s2015 |||| o||u| ||||||eng d | ||
| 020 | |a 9781139924160 |c Online |9 978-1-139-92416-0 | ||
| 024 | 7 | |a 10.1017/CBO9781139924160 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9781139924160 | ||
| 035 | |a (OCoLC)967678778 | ||
| 035 | |a (DE-599)BVBBV043940245 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 530.13 |2 23 | |
| 100 | 1 | |a Garban, Christophe |d 1982- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Noise sensitivity of boolean functions and percolation |c Christophe Garban, ICJ, Université Lyon, Jeffrey E. Steif, Chalmers University of Technology, Gothenberg |
| 246 | 1 | 3 | |a Noise Sensitivity of Boolean Functions & Percolation |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2015 | |
| 300 | |a 1 online resource (xvii, 203 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Institute of Mathematical Statistics textbooks |v 5 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 520 | |a This is a graduate-level introduction to the theory of Boolean functions, an exciting area lying on the border of probability theory, discrete mathematics, analysis, and theoretical computer science. Certain functions are highly sensitive to noise; this can be seen via Fourier analysis on the hypercube. The key model analyzed in depth is critical percolation on the hexagonal lattice. For this model, the critical exponents, previously determined using the now-famous Schramm–Loewner evolution, appear here in the study of sensitivity behavior. Even for this relatively simple model, beyond the Fourier-analytic set-up, there are three crucially important but distinct approaches: hypercontractivity of operators, connections to randomized algorithms, and viewing the spectrum as a random Cantor set. This book assumes a basic background in probability theory and integration theory. Each chapter ends with exercises, some straightforward, some challenging | ||
| 650 | 4 | |a Statistical physics / Textbooks | |
| 650 | 4 | |a Percolation (Statistical physics) / Textbooks | |
| 650 | 4 | |a Algebra, Boolean / Textbooks | |
| 700 | 1 | |a Steif, Jeffrey E. |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-1-107-07643-3 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-1-107-43255-0 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9781139924160 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029349215 | ||
| 966 | e | |u https://doi.org/10.1017/CBO9781139924160 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9781139924160 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176880546349056 |
|---|---|
| any_adam_object | |
| author | Garban, Christophe 1982- |
| author_facet | Garban, Christophe 1982- |
| author_role | aut |
| author_sort | Garban, Christophe 1982- |
| author_variant | c g cg |
| building | Verbundindex |
| bvnumber | BV043940245 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9781139924160 (OCoLC)967678778 (DE-599)BVBBV043940245 |
| dewey-full | 530.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13 |
| dewey-search | 530.13 |
| dewey-sort | 3530.13 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| doi_str_mv | 10.1017/CBO9781139924160 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02881nmm a2200457zcb4500</leader><controlfield tag="001">BV043940245</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2015 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139924160</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-139-92416-0</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9781139924160</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9781139924160</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)967678778</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043940245</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">530.13</subfield><subfield code="2">23</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Garban, Christophe</subfield><subfield code="d">1982-</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Noise sensitivity of boolean functions and percolation</subfield><subfield code="c">Christophe Garban, ICJ, Université Lyon, Jeffrey E. Steif, Chalmers University of Technology, Gothenberg</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">Noise Sensitivity of Boolean Functions & Percolation</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2015</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xvii, 203 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">Institute of Mathematical Statistics textbooks</subfield><subfield code="v">5</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="520" ind1=" " ind2=" "><subfield code="a">This is a graduate-level introduction to the theory of Boolean functions, an exciting area lying on the border of probability theory, discrete mathematics, analysis, and theoretical computer science. Certain functions are highly sensitive to noise; this can be seen via Fourier analysis on the hypercube. The key model analyzed in depth is critical percolation on the hexagonal lattice. For this model, the critical exponents, previously determined using the now-famous Schramm–Loewner evolution, appear here in the study of sensitivity behavior. Even for this relatively simple model, beyond the Fourier-analytic set-up, there are three crucially important but distinct approaches: hypercontractivity of operators, connections to randomized algorithms, and viewing the spectrum as a random Cantor set. This book assumes a basic background in probability theory and integration theory. Each chapter ends with exercises, some straightforward, some challenging</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Statistical physics / Textbooks</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Percolation (Statistical physics) / Textbooks</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebra, Boolean / Textbooks</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Steif, Jeffrey E.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-1-107-07643-3</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-1-107-43255-0</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9781139924160</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:BVB01-029349215</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9781139924160</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/CBO9781139924160</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.BV043940245 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:13Z |
| institution | BVB |
| isbn | 9781139924160 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349215 |
| oclc_num | 967678778 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xvii, 203 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Institute of Mathematical Statistics textbooks |
| spelling | Garban, Christophe 1982- Verfasser aut Noise sensitivity of boolean functions and percolation Christophe Garban, ICJ, Université Lyon, Jeffrey E. Steif, Chalmers University of Technology, Gothenberg Noise Sensitivity of Boolean Functions & Percolation Cambridge Cambridge University Press 2015 1 online resource (xvii, 203 pages) txt rdacontent c rdamedia cr rdacarrier Institute of Mathematical Statistics textbooks 5 Title from publisher's bibliographic system (viewed on 05 Oct 2015) This is a graduate-level introduction to the theory of Boolean functions, an exciting area lying on the border of probability theory, discrete mathematics, analysis, and theoretical computer science. Certain functions are highly sensitive to noise; this can be seen via Fourier analysis on the hypercube. The key model analyzed in depth is critical percolation on the hexagonal lattice. For this model, the critical exponents, previously determined using the now-famous Schramm–Loewner evolution, appear here in the study of sensitivity behavior. Even for this relatively simple model, beyond the Fourier-analytic set-up, there are three crucially important but distinct approaches: hypercontractivity of operators, connections to randomized algorithms, and viewing the spectrum as a random Cantor set. This book assumes a basic background in probability theory and integration theory. Each chapter ends with exercises, some straightforward, some challenging Statistical physics / Textbooks Percolation (Statistical physics) / Textbooks Algebra, Boolean / Textbooks Steif, Jeffrey E. Sonstige oth Erscheint auch als Druckausgabe 978-1-107-07643-3 Erscheint auch als Druckausgabe 978-1-107-43255-0 https://doi.org/10.1017/CBO9781139924160 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Garban, Christophe 1982- Noise sensitivity of boolean functions and percolation Statistical physics / Textbooks Percolation (Statistical physics) / Textbooks Algebra, Boolean / Textbooks |
| title | Noise sensitivity of boolean functions and percolation |
| title_alt | Noise Sensitivity of Boolean Functions & Percolation |
| title_auth | Noise sensitivity of boolean functions and percolation |
| title_exact_search | Noise sensitivity of boolean functions and percolation |
| title_full | Noise sensitivity of boolean functions and percolation Christophe Garban, ICJ, Université Lyon, Jeffrey E. Steif, Chalmers University of Technology, Gothenberg |
| title_fullStr | Noise sensitivity of boolean functions and percolation Christophe Garban, ICJ, Université Lyon, Jeffrey E. Steif, Chalmers University of Technology, Gothenberg |
| title_full_unstemmed | Noise sensitivity of boolean functions and percolation Christophe Garban, ICJ, Université Lyon, Jeffrey E. Steif, Chalmers University of Technology, Gothenberg |
| title_short | Noise sensitivity of boolean functions and percolation |
| title_sort | noise sensitivity of boolean functions and percolation |
| topic | Statistical physics / Textbooks Percolation (Statistical physics) / Textbooks Algebra, Boolean / Textbooks |
| topic_facet | Statistical physics / Textbooks Percolation (Statistical physics) / Textbooks Algebra, Boolean / Textbooks |
| url | https://doi.org/10.1017/CBO9781139924160 |
| work_keys_str_mv | AT garbanchristophe noisesensitivityofbooleanfunctionsandpercolation AT steifjeffreye noisesensitivityofbooleanfunctionsandpercolation AT garbanchristophe noisesensitivityofbooleanfunctionspercolation AT steifjeffreye noisesensitivityofbooleanfunctionspercolation |