Gaussian processes on trees: from spin glasses to branching Brownian motion
Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of mean-field spin glasses in statistical mechanics. Starting with a concise re...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2017
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
163 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers Inhaltsverzeichnis |
| Zusammenfassung: | Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of mean-field spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to mean-field spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the F-KPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a self-contained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 02 Dec 2016) |
| Beschreibung: | 1 online resource (x, 200 pages) |
| ISBN: | 9781316675779 |
| DOI: | 10.1017/9781316675779 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043997587 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 170113s2017 |||| o||u| ||||||eng d | ||
| 020 | |a 9781316675779 |9 978-1-316-67577-9 | ||
| 024 | 7 | |a 10.1017/9781316675779 |2 doi | |
| 035 | |a (OCoLC)969663043 | ||
| 035 | |a (DE-599)BVBBV043997587 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 519.2/3 | |
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 100 | 1 | |a Bovier, Anton |d 1957- |0 (DE-588)109223829 |4 aut | |
| 245 | 1 | 0 | |a Gaussian processes on trees |b from spin glasses to branching Brownian motion |c Anton Bovier, University of Bonn, Germany |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2017 | |
| 300 | |a 1 online resource (x, 200 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Cambridge studies in advanced mathematics |v 163 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 02 Dec 2016) | ||
| 520 | |a Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of mean-field spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to mean-field spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the F-KPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a self-contained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics | ||
| 650 | 4 | |a Gaussian processes | |
| 650 | 4 | |a Random variables | |
| 650 | 0 | 7 | |a Gauß-Prozess |0 (DE-588)4156111-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spinglas |0 (DE-588)4138228-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Brownsche Bewegung |0 (DE-588)4128328-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zufallsvariable |0 (DE-588)4129514-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gauß-Prozess |0 (DE-588)4156111-9 |D s |
| 689 | 0 | 1 | |a Zufallsvariable |0 (DE-588)4129514-6 |D s |
| 689 | 0 | 2 | |a Spinglas |0 (DE-588)4138228-6 |D s |
| 689 | 0 | 3 | |a Brownsche Bewegung |0 (DE-588)4128328-4 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-1-107-16049-1 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/9781316675779 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029405620&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029405620 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u http://doi.org/10.1017/9781316675779 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/9781316675779 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176976454352896 |
|---|---|
| adam_text | Titel: Gaussian processes on trees
Autor: Bovier, Anton
Jahr: 2017
Gaussian Processes on Trees From Spin Glasses to Branching Brownian Motion / ANTON/BOVIER University of Borin, Germany Cambridge UNIVERSITY PRESS
Contents Preface page vii Acknowledgements x 1 Extreme Value Theory for iid Sequences 1 1.1 Basic Issues 1 1.2 Extremal Distributions 2 1.3 Level-Crossings and kth Maxima 12 1.4 Bibliographic Notes 13 2 Extrema] Processes 15 2.1 Point Processes 15 2.2 Laplace functionals 18 2.3 Poisson Point Processes 19 2.4 Convergence of Point Processes 21 2.5 Point Processes of Extremes 29 2.6 Bibliographic Notes 33 3 Normal Sequences 34 3.1 Normal Comparison 35 3.2 Applications to Extremes 42 3.3 Bibliographic Notes 44 4 Spin Glasses 45 4.1 Setting and Examples 45 4.2 The REM 47 4.3 The GREM, Two Levels 49 4.4 Connection to Branching Brownian Motion 54 4.5 The Galton-Watson Process 55 4.6 The REM on the Galton-Watson Tree 57 4.7 Bibliographic Notes 59 v
Contents vi 5 Branching Brownian Motion 60 5.1 Definition and Basics 60 5.2 Rough Heuristics 61 5.3 Recursion Relations 63 5.4 The F-KPP Equation 65 5.5 The Travelling Wave 67 5.6 The Derivative Martingale 70 5.7 Bibliographic Notes 75 6 Bramson’s Analysis of the F-KPP Equation 76 6.1 Feynman-Kac Representation 76 6.2 The Maximum Principle and its Applications 80 6.3 Estimates on the Linear F-KPP Equation 95 6.4 Brownian Bridges 98 6.5 Hitting Probabilities of Curves 102 6.6 Asymptotics of Solutions of the F-KPP Equation 105 6.7 Convergence Results 112 6.8 Bibliographic Notes 121 7 The Extremal Process of BBM 122 7.1 Limit Theorems for Solutions 122 7.2 Existence of a Limiting Process 127 7.3 Interpretation as Cluster Point Process 132 7.4 Bibliographic Notes 144 8 Full Extremal Process 145 8.1 The Embedding 145 8.2 Properties of the Embedding 147 8.3 The ^-Thinning 149 8.4 Bibliographic Notes 152 9 Variable Speed BBM 153 9.1 The Construction 153 9.2 Two-Speed BBM 154 9.3 Universality Below the Straight Line 176 9.4 Bibliographic Notes 189 References Index 191 199
|
| any_adam_object | 1 |
| author | Bovier, Anton 1957- |
| author_GND | (DE-588)109223829 |
| author_facet | Bovier, Anton 1957- |
| author_role | aut |
| author_sort | Bovier, Anton 1957- |
| author_variant | a b ab |
| building | Verbundindex |
| bvnumber | BV043997587 |
| classification_rvk | SK 820 |
| collection | ZDB-20-CBO |
| ctrlnum | (OCoLC)969663043 (DE-599)BVBBV043997587 |
| dewey-full | 519.2/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/3 |
| dewey-search | 519.2/3 |
| dewey-sort | 3519.2 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/9781316675779 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03363nmm a2200541zcb4500</leader><controlfield tag="001">BV043997587</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">170113s2017 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781316675779</subfield><subfield code="9">978-1-316-67577-9</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/9781316675779</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)969663043</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043997587</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">519.2/3</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">Bovier, Anton</subfield><subfield code="d">1957-</subfield><subfield code="0">(DE-588)109223829</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Gaussian processes on trees</subfield><subfield code="b">from spin glasses to branching Brownian motion</subfield><subfield code="c">Anton Bovier, University of Bonn, Germany</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2017</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (x, 200 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">Cambridge studies in advanced mathematics</subfield><subfield code="v">163</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 02 Dec 2016)</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of mean-field spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to mean-field spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the F-KPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a self-contained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gaussian processes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Random variables</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gauß-Prozess</subfield><subfield code="0">(DE-588)4156111-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Spinglas</subfield><subfield code="0">(DE-588)4138228-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Brownsche Bewegung</subfield><subfield code="0">(DE-588)4128328-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zufallsvariable</subfield><subfield code="0">(DE-588)4129514-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Gauß-Prozess</subfield><subfield code="0">(DE-588)4156111-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Zufallsvariable</subfield><subfield code="0">(DE-588)4129514-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Spinglas</subfield><subfield code="0">(DE-588)4138228-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Brownsche Bewegung</subfield><subfield code="0">(DE-588)4128328-4</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">978-1-107-16049-1</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/9781316675779</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029405620&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</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:BVB01-029405620</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">http://doi.org/10.1017/9781316675779</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/10.1017/9781316675779</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.BV043997587 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:40:44Z |
| institution | BVB |
| isbn | 9781316675779 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029405620 |
| oclc_num | 969663043 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (x, 200 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Bovier, Anton 1957- (DE-588)109223829 aut Gaussian processes on trees from spin glasses to branching Brownian motion Anton Bovier, University of Bonn, Germany Cambridge Cambridge University Press 2017 1 online resource (x, 200 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 163 Title from publisher's bibliographic system (viewed on 02 Dec 2016) Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of mean-field spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to mean-field spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the F-KPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a self-contained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics Gaussian processes Random variables Gauß-Prozess (DE-588)4156111-9 gnd rswk-swf Spinglas (DE-588)4138228-6 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Gauß-Prozess (DE-588)4156111-9 s Zufallsvariable (DE-588)4129514-6 s Spinglas (DE-588)4138228-6 s Brownsche Bewegung (DE-588)4128328-4 s 1\p DE-604 Erscheint auch als Druckausgabe 978-1-107-16049-1 https://doi.org/10.1017/9781316675779 Verlag URL des Erstveröffentlichers Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029405620&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bovier, Anton 1957- Gaussian processes on trees from spin glasses to branching Brownian motion Gaussian processes Random variables Gauß-Prozess (DE-588)4156111-9 gnd Spinglas (DE-588)4138228-6 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Zufallsvariable (DE-588)4129514-6 gnd |
| subject_GND | (DE-588)4156111-9 (DE-588)4138228-6 (DE-588)4128328-4 (DE-588)4129514-6 |
| title | Gaussian processes on trees from spin glasses to branching Brownian motion |
| title_auth | Gaussian processes on trees from spin glasses to branching Brownian motion |
| title_exact_search | Gaussian processes on trees from spin glasses to branching Brownian motion |
| title_full | Gaussian processes on trees from spin glasses to branching Brownian motion Anton Bovier, University of Bonn, Germany |
| title_fullStr | Gaussian processes on trees from spin glasses to branching Brownian motion Anton Bovier, University of Bonn, Germany |
| title_full_unstemmed | Gaussian processes on trees from spin glasses to branching Brownian motion Anton Bovier, University of Bonn, Germany |
| title_short | Gaussian processes on trees |
| title_sort | gaussian processes on trees from spin glasses to branching brownian motion |
| title_sub | from spin glasses to branching Brownian motion |
| topic | Gaussian processes Random variables Gauß-Prozess (DE-588)4156111-9 gnd Spinglas (DE-588)4138228-6 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Zufallsvariable (DE-588)4129514-6 gnd |
| topic_facet | Gaussian processes Random variables Gauß-Prozess Spinglas Brownsche Bewegung Zufallsvariable |
| url | https://doi.org/10.1017/9781316675779 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029405620&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bovieranton gaussianprocessesontreesfromspinglassestobranchingbrownianmotion |