Mean field models for spin glasses: 1 Basic examples
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
Folge 3 ; 54 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 485 Seiten |
| ISBN: | 9783642152016 9783642152023 |
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MARC
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Record in the Search Index
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IMAGE 1
CONTENTS
INTRODUCTION XI
1. THE SHERRINGTON-KIRKPATRICK MODEL 1
1.1 INTRODUCTION 1
1.2 NOTATIONS AND SIMPLE FACTS 5
1.3 GAUSSIAN INTERPOLATION AND THE SMART PATH METHOD 12 1.4 LATALA'S
ARGUMENT 29
1.5 A KIND OF CENTRAL LIMIT THEOREM 51
1.6 THE CAVITY METHOD 53
1.7 GIBBS' MEASURE; THE TAP EQUATIONS 67
1.8 SECOND MOMENT COMPUTATIONS AND THE ALMEIDA-THOULESS LINE 80 1.9
BEYOND THE AT LINE 93
1.10 CENTRAL LIMIT THEOREM FOR THE OVERLAPS 98
1.11 NON GAUSSIAN BEHAVIOR: HANEN'S THEOREM 113
1.12 THE SK MODEL WITH D-COMPONENT SPINS 125
1.13 THE PHYSICIST'S REPLICA METHOD 140
1.14 NOTES AND COMMENTS 146
2. THE PERCEPTRON MODEL 151
2.1 INTRODUCTION 151
2.2 THE SMART PATH 154
2.3 CAVITY IN M 160
2.4 THE REPLICA SYMMETRIC SOLUTION 173
2.5 EXPONENTIAL INEQUALITIES 182
2.6 NOTES AND COMMENTS 190
3. THE SHCHERBINA AND TIROZZI MODEL 191
3.1 THE POWER OF CONVEXITY 191
3.2 THE REPLICA-SYMMETRIC EQUATIONS 207
3.3 CONTROLLING THE SOLUTIONS OF THE RS EQUATIONS 224
3.4 NOTES AND COMMENTS 235
VII
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1004409982
DIGITALISIERT DURCH
IMAGE 2
VIII CONTENTS
4. THE HOPFIELD MODEL 237
4.1 INTRODUCTION: THE CURIE-WEISS MODEL 237
4.2 LOCAL CONVEXITY AND THE HUBBARD-STRATONOVITCH TRANSFORM . 244 4.3
THE BOVIER-GAYRARD LOCALIZATION THEOREM 254
4.4 SELECTING A STATE WITH AN EXTERNAL FIELD 272
4.5 CONTROLLING THE OVERLAPS 274
4.6 APPROXIMATE INTEGRATION BY PARTS AND THE REPLICA-SYMMETRIC EQUATIONS
284
4.7 NOTES AND COMMENTS 295
5. THE V-STATISTICS MODEL 297
5.1 INTRODUCTION 297
5.2 THE SMART PATH 299
5.3 CAVITY IN M 302
5.4 THE NEW EQUATION 306
5.5 THE REPLICA-SYMMETRIC SOLUTION 312
6. THE DILUTED SK MODEL AND THE K-SAT PROBLEM 325
6.1 INTRODUCTION 325
6.2 PURE STATE 328
6.3 THE FUNCTIONAL ORDER PARAMETER 340
6.4 THE REPLICA-SYMMETRIC SOLUTION 345
6.5 THE FRANZ-LEONE BOUND 359
6.6 CONTINUOUS SPINS 364
6.7 THE POWER OF CONVEXITY 376
6.8 NOTES AND COMMENTS 395
7. AN ASSIGNMENT PROBLEM 397
7.1 INTRODUCTION 397
7.2 OVERVIEW OF THE PROOF 401
7.3 THE CAVITY METHOD 402
7.4 DECOUPLING 405
7.5 EMPIRICAL MEASURES 413
7.6 OPERATORS 422
7.7 NOTES AND COMMENTS 433
A. APPENDIX: ELEMENTS OF PROBABILITY THEORY 435
A.I HOW TO USE THIS APPENDIX 435
A.2 DIFFERENTIATION INSIDE AN EXPECTATION 435
A.3 GAUSSIAN RANDOM VARIABLES 437
A.4 GAUSSIAN INTEGRATION BY PARTS 440
A.5 TAIL ESTIMATES 441
A.6 HOW TO USE TAIL ESTIMATES 444
A.7 BERNSTEIN'S INEQUALITY 446
A.8 E-NETS 448
IMAGE 3
CONTENTS IX
A.9 RANDOM MATRICES 449
A. 10 POISSON RANDOM VARIABLES AND POINT PROCESSES 454
A. 11 DISTANCES BETWEEN PROBABILITY MEASURES 456
A.12 THE PALEY-ZYGMUND INEQUALITY 460
A.13 DIFFERENTIAL INEQUALITIES 460
A.14 THE LATALA-GUERRA LEMMA 461
A.15 PROOF OF THEOREM 3.1.4 462
REFERENCES 465
INDEX 475
GLOSSARY 479 |
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| isbn | 9783642152016 9783642152023 |
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| spelling | Talagrand, Michel 1952- Verfasser (DE-588)112924379 aut Mean field models for spin glasses 1 Basic examples Michel Talagrand Berlin [u.a.] Springer 2011 XVIII, 485 Seiten txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete : Folge 3 54 Ergebnisse der Mathematik und ihrer Grenzgebiete : Folge 3 ... (DE-604)BV036859189 1 Ergebnisse der Mathematik und ihrer Grenzgebiete Folge 3 ; 54 (DE-604)BV000899194 54 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020775014&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Talagrand, Michel 1952- Mean field models for spin glasses Ergebnisse der Mathematik und ihrer Grenzgebiete |
| title | Mean field models for spin glasses |
| title_auth | Mean field models for spin glasses |
| title_exact_search | Mean field models for spin glasses |
| title_full | Mean field models for spin glasses 1 Basic examples Michel Talagrand |
| title_fullStr | Mean field models for spin glasses 1 Basic examples Michel Talagrand |
| title_full_unstemmed | Mean field models for spin glasses 1 Basic examples Michel Talagrand |
| title_short | Mean field models for spin glasses |
| title_sort | mean field models for spin glasses basic examples |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020775014&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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