Random walks, random fields, and disordered systems:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham [u.a.]
Springer
2015
|
| Series: | Lecture notes in mathematics
2144 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 239 S. graph. Darst. |
| ISBN: | 9783319193380 |
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MARC
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Record in the Search Index
| _version_ | 1804175322283769856 |
|---|---|
| adam_text | Anton Bovier • David Brydges •
Amin Coja-Oghlan • Dmitry Ioffe •
Gregory F Lawler
Random Walks,
Random Fields,
and Disordered Systems
V
Marek Biskup • Jiff Cemy • Roman Kotecky
Editors
Springer
Contents
From Spin Glasses to Branching Brownian Motion—and Back? 1
Anton Bovier
1 Introduction 1
2 Spin Glasses 2
2 1 Setting and Examples 2
2 2 Classical Extreme Value Theory, Aka the REM 4
2 3 Rough Estimates, the Second Moment Method 4
2 4 The GREM, Two Levels 8
3 Branching Brownian Motion 13
3 1 Definition and Basics 13
3 2 The F-KPP Equation 15
3 3 The Travelling Wave 16
3 4 The Derivative Martingale 20
4 The Extremal Process of BBM 25
4 1 Controlling Solutions of the F-KPP Equation 25
4 2 Existence of a Limiting Process 34
4 3 Flash Back to the Derivative Martingale 37
44A Representation for the Laplace Functional 38
4 5 Interpretation as Cluster Point Process 41
5 Variable Speed BBM 50
References 62
The Renormalization Group and Self-avoiding Walk 65
David Brydges
1 Introduction 65
2 The Lattice Edwards Model 68
3 The Free Field and Local Time 71
4 The Free Field, Local Time and Differential Forms 74
4 1 Review of Differential Forms 74
4 2 Gaussian Integrals in Terms of Forms 77
4 3 The Local Time Isomorphism and Forms 79
IX
Contents
5 Susceptibility as a Gaussian Integral 80
5 1 The Most General Split into Gaussian Plus Perturbation 81
5 2 The Proof of Theorem 2 2 83
5 3 The Susceptibility in Terms of Super-Convolution 85
6 The Renormalisation Group 88
6 1 Progressive Integration 90
6 2 First Order Perturbation Theory 90
6 3 Second Order Perturbation Theory 92
6 4 The Error Coordinate 94
7 The Norm of the Error Coordinate 101
7 1 The J£ Norm 101
7 2 The Irrelevant Parts of K+ 103
7 3 The Complete Recursion 108
8 Outline of Proof of Theorem 5 2 110
8 1 Construction of Zq, Uq 110
8 2 Coupling Constants at Large Scales Ill
8 3 Proof of (73) 112
8 4 Proof of (74) 113
References 114
Phase Transitions in Discrete Structures 117
Amin Coja-Oghlan
1 Introduction 117
2 The Cavity Method 118
2 1 Basic Concepts 118
2 2 Belief Propagation 120
2 3 Disordered Systems 123
2 4 The Replica Symmetric Ansatz 125
2 5 Replica Symmetry Breaking 128
3 Classical Rigorous Results 132
3 1 Basics 132
3 2 The “Vanilla” Second Moment Method 134
4 A Physics-Enhanced Rigorous Approach 137
4 1 Quiet Planting 138
4 2 Condensation * 140
4 3 The Asymptotic 2-Colorability Threshold 142
5 Conclusions and Outlook 144
References 145
Multidimensional Random Polymers: A Renewal Approach 147
Dmitry Ioffe
1 Introduction 147
1 1 Class of Models 148
1 2 Morphology 149
Contents xi
2 Thermodynamics of Annealed and Quenched Models 153
2 1 Annealed Models in Dimensions d 2 154
2 2 Thermodynamics of Quenched Polymers 163
3 Multidimensional Renewal Theory and Annealed Polymers 165
3 1 Multi-Dimensional Renewal Theory 165
3 2 Ballistic Phase of Annealed Polymers 174
4 Very Weak Disorder in d 4 185
5 Strong Disorder 194
References 209
Loop Measures and the Gaussian Free Field 211
Gregory F Lawler and Jacob Perlman
1 Introduction 211
2 Definitions 212
3 Loop Measures 215
3 1 Definition 215
3 2 Relation to Loop-Erased Walk 218
4 Loop Soup and Gaussian Free Field 220
4 1 Soups 220
4 2 Loop Soup 221
43A Continuous Occupation Field 223
4 4 Trivial Loops 227
4 5 Relation to the Real Gaussian Free Field 229
4 6 Complex Weights 230
References 235
|
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| id | DE-604.BV042985545 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:14:27Z |
| institution | BVB |
| isbn | 9783319193380 |
| language | English |
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| physical | XIII, 239 S. graph. Darst. |
| publishDate | 2015 |
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| publishDateSort | 2015 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Bovier, Anton 1957- Verfasser (DE-588)109223829 aut Random walks, random fields, and disordered systems Anton Bovier ; David Brydges ; Amin Coja-Oghlan ... Marek Biskup ; Jiří Černý ; Roman Kotecký, eds. Cham [u.a.] Springer 2015 XIII, 239 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2144 Brydges, David C. Verfasser (DE-588)139522581 aut Coja-Oghlan, Amin 1975- Verfasser (DE-588)123551994 aut Biskup, Marek 1971- Sonstige (DE-588)138164320 oth Černý, Jiří 1975- Sonstige (DE-588)1031769390 oth Kotecký, Roman Sonstige (DE-588)138164657 oth Erscheint auch als Online-Ausgabe 978-3-319-19339-7 Lecture notes in mathematics 2144 (DE-604)BV000676446 2144 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028410876&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bovier, Anton 1957- Brydges, David C. Coja-Oghlan, Amin 1975- Random walks, random fields, and disordered systems Lecture notes in mathematics |
| title | Random walks, random fields, and disordered systems |
| title_auth | Random walks, random fields, and disordered systems |
| title_exact_search | Random walks, random fields, and disordered systems |
| title_full | Random walks, random fields, and disordered systems Anton Bovier ; David Brydges ; Amin Coja-Oghlan ... Marek Biskup ; Jiří Černý ; Roman Kotecký, eds. |
| title_fullStr | Random walks, random fields, and disordered systems Anton Bovier ; David Brydges ; Amin Coja-Oghlan ... Marek Biskup ; Jiří Černý ; Roman Kotecký, eds. |
| title_full_unstemmed | Random walks, random fields, and disordered systems Anton Bovier ; David Brydges ; Amin Coja-Oghlan ... Marek Biskup ; Jiří Černý ; Roman Kotecký, eds. |
| title_short | Random walks, random fields, and disordered systems |
| title_sort | random walks random fields and disordered systems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028410876&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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