Probability in complex physical systems in honour of Erwin Bolthausen and Jürgen Gärtner
Gespeichert in:
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| Sprache: | English |
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Heidelberg [u.a.]
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2012
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| Schriftenreihe: | Springer proceedings in mathematics
11 |
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| 245 | 1 | 0 | |a Probability in complex physical systems |b in honour of Erwin Bolthausen and Jürgen Gärtner |c Jean-Dominique Deuschel ... ed. |
| 264 | 1 | |a Heidelberg [u.a.] |b Springer |c 2012 | |
| 300 | |a XIX, 512 S. |b Ill., graph. Darst. | ||
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| 490 | 1 | |a Springer proceedings in mathematics |v 11 | |
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| 700 | 1 | |a Deuschel, Jean-Dominique |d 1957- |e Sonstige |0 (DE-588)129802956 |4 oth | |
| 700 | 1 | |a Bolthausen, Erwin |d 1945- |0 (DE-588)108913035X |4 hnr | |
| 700 | 1 | |a Gärtner, Jürgen |d 1950- |0 (DE-588)108963269X |4 hnr | |
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Datensatz im Suchindex
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|---|---|
| adam_text | IMAGE 1
CONTENTS
LAUDATIO: THE MATHEMATICAL WORK O F JIIRGEN GARTNER 1
FRANK DEN HOLLANDER 1 GARTNER-ELLIS LARGE DEVIATION PRINCIPLE 1
2 KOLMOGOROV-PETROVSKII-PISKUNOV EQUATION 3
3 DAWSON-GARTNER PROJECTIVE LIMIT LARGE DEVIATION PRINCIPLE 4
4 MCKEAN-VLASOV EQUATION 5
5 PARABOLIC ANDERSON MODEL 6
6 PERSONAL REMARKS 8
REFERENCES 9
PART I THE PARABOLIC ANDERSON MODEL
THE PARABOLIC ANDERSON MODEL WITH LONG RANGE BASIC HAMILTONIAN AND
WEIBULL TYPE RANDOM POTENTIAL 13
STANISLAV MOLCHANOV AND HAO ZHANG 1 DEDICATION AND INTRODUCTION 13
2 THE ANNEALED AND QUENCHED ASYMPTOTIC PROPERTIES O F U(T, 0) WITH
WEIBULL POTENTIAL V ( X , CO M ): P{V{-) X } = EXP { - . . . 2 0
3 THE ANNEALED AND QUENCHED ASYMPTOTIC PROPERTIES OF U(T, 0) WITH
POTENTIAL V{X,U M ) O F THE FORM L {V{.) ,V[ - E X P { - ; ; / . ( .
V ) } 23
4 CONCLUDING REMARK 30
REFERENCES 3 0
PARABOLIC ANDERSON MODEL WITH VOTER CATALYSTS: DICHOTOMY IN THE BEHAVIOR
O F LYAPUNOV EXPONENTS 33
GREGORY MAILLARD, THOMAS MOUNTFORD, AND SAMUEL SCHOPFER 1 INTRODUCTION
34
1.1 MODEL 34
1.2 VOTER MODEL 34
1.3 LYAPUNOV EXPONENTS 35
1.4 MAIN RESULTS 38
XI
HTTP://D-NB.INFO/1014072530
IMAGE 2
XII C O N T E N T S
2 PROOF O F THEOREMS 1.1 AND 1.3 39
2.1 COARSE-GRAINING AND SKELETONS 4 0
2.2 THE BAD ENVIRONMENT SET B E 42
2.3 THE BAD RANDOM WALK SET BW 4 8
2.4 PROOF OF THEOREM 1.1 51
3 PROOF O F THEOREM 1.4 51
4 PROOF OF THEOREM 1.4 62
REFERENCES 67
PRECISE ASYMPTOTICS FOR THE PARABOLIC ANDERSON MODEL WITH A MOVING
CATALYST OR TRAP 6 9
ADRIAN SCHNITZLER AND TILMAN WOLFF 1 INTRODUCTION 7 0
2 MOVING TRAP 73
2.1 LOCALIZED INITIAL CONDITION 7 4
2.2 HOMOGENEOUS INITIAL CONDITION 7 5
3 MOVING CATALYST 79
3.1 SPECTRAL PROPERTIES OF HIGHER-ORDER ANDERSON HAMILTONIANS 8 0 3.2
APPLICATION TO ANNEALED HIGHER MOMENT ASYMPTOTICS 87
REFERENCES 88
PARABOLIC ANDERSON MODEL WITH A FINITE NUMBER O F MOVING CATALYSTS 91
FABIENNE CASTELL, ONUR GUN, AND GREGORY MAILLARD 1 INTRODUCTION 9 2
1.1 MODEL 92
1.2 LYAPUNOV EXPONENTS AND INTERMITTENCY 93
1.3 LITERATURE 94
1.4 MAIN RESULTS 95
1.5 DISCUSSION 99
2 PROOF OF THEOREM 1.1 100
3 PROOF O F THEOREMS 1.2-1.3 106
3.1 PROOF OF THEOREM 1.2 106
3.2 PROOF O F THEOREM 1.3 107
4 PROOF OF THEOREM 1.4 108
5 PROOF O F COROLLARY 1.1 110
APPENDIX I L L
REFERENCES 116
SURVIVAL PROBABILITY O F A RANDOM WALK AMONG A POISSON SYSTEM O F MOVING
TRAPS 119
ALEXANDER DREWITZ, JIIRGEN GARTNER, ALEJANDRO F. RAMIREZ, AND RONGFENG
SUN 1 INTRODUCTION 120
1.1 MODEL AND RESULTS 120
1.2 RELATION TO THE PARABOLIC ANDERSON MODEL 122
IMAGE 3
CONTENTS XIII
1.3 REVIEW OF RELATED RESULTS 123
1.4 OUTLINE 125
2 ANNEALED SURVIVAL PROBABILITY 126
2.1 EXISTENCE OF THE ANNEALED LYAPUNOV EXPONENT 126
2.2 SPECIAL CASE K = 0 128
2.3 LOWER BOUND ON THE ANNEALED SURVIVAL PROBABILITY 131
2.4 UPPER BOUND ON THE ANNEALED SURVIVAL PROBABILITY. THE PASCAL
PRINCIPLE 133
3 QUENCHED AND SEMI-ANNEALED UPPER BOUNDS 138
4 EXISTENCE AND POSITIVITY O F THE QUENCHED LYAPUNOV EXPONENT 144
4.1 SHAPE THEOREM AND THE QUENCHED LYAPUNOV EXPONENT 144
4.2 PROOF O F SHAPE THEOREM FOR BOUNDED ERGODIC POTENTIALS 148
4.3 EXISTENCE O F THE QUENCHED LYAPUNOV EXPONENT FOR THE PAM 151 4.4
POSITIVITY O F THE QUENCHED LYAPUNOV EXPONENT 154
REFERENCES 157
QUENCHED LYAPUNOV EXPONENT FOR THE PARABOLIC ANDERSON MODEL IN A DYNAMIC
RANDOM ENVIRONMENT 159
JIIRGEN GARTNER, FRANK DEN HOLLANDER, AND GREGORY MAILLARD 1
INTRODUCTION 160
1.1 PARABOLIC ANDERSON MODEL 160
1.2 LYAPUNOV EXPONENTS 162
1.3 LITERATURE 163
1.4 MAIN RESULTS 167
1.5 DISCUSSION AND OPEN PROBLEMS 168
2 PROOF O F THEOREMS 1.1-1.3 170
2.1 PROOF OF THEOREM 1.1 170
2.2 PROOF O F THEOREM 1.2(I) 171
2.3 PROOF O F THEOREM 1.2(II) 173
2.4 PROOF O F THEOREM 1.2(III) 177
2.5 PROOF O F THEOREM 1.3(I) 179
2.6 PROOF O F THEOREM 1.3(III) 180
2.7 PROOF O F THEOREM 1.3(II) 186
3 PROOF OF THEOREMS 1.4-1.6 189
3.1 PROOF O F THEOREM 1.4 189
3.2 PROOF O F THEOREM 1.5 189
3.3 PROOF O F THEOREM 1.6 191
REFERENCES 192
ASYMPTOTIC SHAPE AND PROPAGATION O F FRONTS FOR GROWTH MODELS IN DYNAMIC
RANDOM ENVIRONMENT 195
HARRY KESTEN, ALEJANDRO F. RAMIREZ, AND VLADAS SIDORAVICIUS 1
INTRODUCTION 195
2 SPREAD O F AN INFECTION IN A MOVING POPULATION ( D A 0, D B 0 )
199
2.1 SHAPE THEOREM 199
2.2 PHASE TRANSITION 206
IMAGE 4
X I V C O N T E N T S
3 THE STOCHASTIC COMBUSTION PROCESS ( DA = 0, D G 0) 208
3.1 SHAPE THEOREM 208
3.2 THE STOCHASTIC COMBUSTION PROCESS IN DIMENSION D = 1 209
3.3 ACTIVATED RANDOM WALKS MODEL AND ABSORBING STATE PHASE TRANSITION
215
4 MODIFIED DIFFUSION LIMITED AGGREGATION ( D A 0, D K - 0) 216
REFERENCES 222
THE PARABOLIC ANDERSON MODEL WITH ACCELERATION AND DECELERATION 225
WOLFGANG KONIG AND SYLVIA SCHMIDT 1 INTRODUCTION 225
2 ASSUMPTIONS AND PRELIMINARIES 227
2.1 MODEL ASSUMPTIONS 227
2.2 VARIATIONAL FORMULAS 228
3 RESULTS 230
3.1 FIVE PHASES 230
3.2 MOMENT ASYMPTOTICS 231
3.3 VARIATIONAL CONVERGENCE 232
4 PROOF O F VARIATIONAL CONVERGENCE (PROPOSITION 3.3) 233
5 PROOF FOR PHASES 1-3 (THEOREM 3.1) 238
6 PROOF FOR PHASE 4 (THEOREM 3.2) 242
REFERENCES 244
A SCALING LIMIT THEOREM FOR THE PARABOLIC ANDERSON MODEL WITH
EXPONENTIAL POTENTIAL 247
HUBERT LACOIN AND PETER MORTERS 1 INTRODUCTION AND MAIN RESULTS 247
1.1 OVERVIEW AND BACKGROUND 247
1.2 STATEMENT O F RESULTS 251
2 PROOF O F THE MAIN RESULTS 252
2.1 OVERVIEW 252
2.2 AUXILIARY RESULTS 254
2.3 UPPER BOUNDS 257
2.4 ANALYSIS O F THE VARIATIONAL PROBLEM 265
2.5 PROOF O F THE ALMOST SURE ASYMPTOTICS 267
2.6 PROOF OF THE WEAK ASYMPTOTICS 268
2.7 PROOF OF THE SCALING LIMIT THEOREM 269
3 CONCLUDING REMARKS 271
REFERENCES 271
PART II SELF-INTERACTING RANDOM WALKS AND POLYMERS
THE STRONG INTERACTION LIMIT O F CONTINUOUS-TIME WEAKLY SELF-AVOIDING
WALK 275
DAVID C. BRYDGES, ANTOINE DAHLQVIST, AND GORDON SLADE 1 DOMB-JOYCE
MODEL: DISCRETE TIME 275
IMAGE 5
CONTENTS X V
2 THE CONTINUOUS-TIME WEAKLY SELF-AVOIDING WALK 277
2.1 FIXED-LENGTH WALKS 278
2.2 TWO-POINT FUNCTION 281
REFERENCES 286
COPOLYMERS AT SELECTIVE INTERFACES: SETTLED ISSUES AND OPEN PROBLEMS 289
FRANCESCO CARAVENNA, GIAMBATTISTA GIACOMIN, AND FABIO LUCIO TONINELLI 1
COPOLYMERS AND SELECTIVE SOLVENTS 289
1.1 A BASIC MODEL 289
1.2 THE (GENERAL) COPOLYMER MODEL 291
1.3 THE FREE ENERGY: LOCALIZATION AND DEREALIZATION 293
1.4 THE PHASE DIAGRAM 294
1.5 THE CRITICAL BEHAVIOR AND A WORD ABOUT PINNING MODELS 298
1.6 ORGANISATION O F THE CHAPTER 299
2 LOCALIZATION ESTIMATES 300
3 DEREALIZATION ESTIMATES 302
3.1 FRACTIONAL MOMENT METHOD: THE GENERAL PRINCIPLE 302
3.2 FRACTIONAL MOMENT METHOD: APPLICATION 303
4 CONTINUUM MODEL AND WEAK COUPLING LIMIT 304
5 PATH PROPERTIES 306
5.1 THE LOCALIZED PHASE 307
5.2 THE DELOCALIZED PHASE 308
REFERENCES 310
SOME LOCALLY SELF-INTERACTING WALKS ON THE INTEGERS 313
ANNA ERSCHLER, BALINT TOTH, AND WENDELIN WERNER 1 INTRODUCTION 313
2 SURVEY OF LEFT-RIGHT SYMMETRIC CASES 318
2.1 WHEN B 0 AND -B/3 A B: THE TRSM REGIME? 318
2.2 WHEN B 0 AND A -B/3: THE STUCK CASE 319
2.3 WHEN B 0 AND A B: THE SLOW PHASE? 320
2.4 THE TWO CRITICAL CASES 322
2.5 STATIONARY MEASURES FOR THE CASES WHERE B 0 AND - B / 3 A B
323
2.6 . SOME COMMENTS 326
3 SOME CASES WITHOUT LEFT-RIGHT SYMMETRY 327
3.1 SETUP AND STATEMENT 327
3.2 THE SCENARIO 329
3.3 AUXILIARY SEQUENCES 331
3.4 THE COUPLING 332
3.5 AN EXAMPLE WITH LOGARITHMIC BEHAVIOUR 334
3.6 BALLISTIC BEHAVIOUR 336
4 SOME OPEN QUESTIONS 337
REFERENCES 338
IMAGE 6
X V I C O N T E N T S
STRETCHED POLYMERS IN RANDOM ENVIRONMENT 339
DMITRY IOFFE AND YVAN VELENIK 1 INTRODUCTION 339
1.1 CLASS O F MODELS 340
1.2 BALLISTIC AND SUB-BALLISTIC PHASES 342
1.3 LYAPUNOV EXPONENTS 343
1.4 VERY WEAK, WEAK, AND STRONG DISORDER 344
2 LARGE DEVIATIONS 345
2.1 RAMIFICATIONS FOR BALLISTIC BEHAVIOR 346
2.2 PROOF O F LEMMA 1 347
3 GEOMETRY O F TYPICAL POLYMERS 348
3.1 SKELETONS O F PATHS 348
3.2 ANNEALED MODELS 349
3.3 QUENCHED MODELS 350
3.4 IRREDUCIBLE DECOMPOSITION AND EFFECTIVE DIRECTED STRUCTURE 354 3.5
BASIC PARTITION FUNCTIONS 355
4 THE ANNEALED MODEL 356
4.1 ASYMPTOTICS O F T = T V , 356
4.2 GEOMETRY O F K , ANNEALED LLN AND CLT 357
4.3 LOCAL LIMIT THEOREM FOR THE ANNEALED POLYMER 358
5 WEAK DISORDER 359
5.1 LLN AT SUPERCRITICAL DRIFTS 359
5.2 VERY WEAK DISORDER 360
5.3 CONVERGENCE O F PARTITION FUNCTIONS 361
5.4 QUENCHED CLT 364
6 STRONG DISORDER 365
6.1 NORMALIZATION 366
6.2 REDUCTION TO BASIC PARTITION FUNCTIONS 366
6.3 FRACTIONAL MOMENTS 367
REFERENCES 368
PART III BRANCHING PROCESSES
MULTISCALE ANALYSIS: FISHER-WRIGHT DIFFUSIONS WITH RARE MUTATIONS AND
SELECTION, LOGISTIC BRANCHING SYSTEM 373
DONALD A. DAWSON AND ANDREAS GREVEN 1 MOTIVATION AND BACKGROUND 374
1.1 OUTLINE 376
2 THE FISHER-WRIGHT MODEL WITH RARE MUTATION AND SELECTION 376
2.1 A TWO-TYPE MEAN-FIELD DIFFUSION MODEL AND ITS DESCRIPTION 376 2.2
TWO TIME WINDOWS FOR THE SPREAD O F THE ADVANTAGEOUS TYPE 378 2.3 THE
EARLY TIME WINDOW AS N -** OO 379
2.4 THE LATE TIME WINDOW AS N - OO 382
IMAGE 7
CONTENTS
X V L L
3 A LOGISTIC BRANCHING RANDOM WALK AND ITS GROWTH 388
3.1 THE LOGISTIC BRANCHING PARTICLE MODEL 388
3.2 THE EARLY TIME WINDOW AS N - OO 390
3.3 THE DROPLET EXPANSION AND CRUMP-MODE-JAGERS PROCESSES 391 3.4 TIME
POINT O F EMERGENCE AS N - OO 394
3.5 THE LATE TIME WINDOW AS N - OO 395
4 THE DUALITY RELATION 398
4.1 A CLASSICAL DUALITY FORMULA 398
4.2 THE GENEALOGY AND DUALITY 400
4.3 THE DUAL FOR GENERAL TYPE SPACE 401
4.4 OUTLOOK ON SET-VALUED DUALS 406
REFERENCES 407
PROPERTIES OF STATES O F SUPER-A-STABLE MOTION WITH BRANCHING O F INDEX
1 + FT 409
KLAUS FLEISCHMANN, LEONID MYTNIK, AND VITALI WACHTEL 1 MODEL:
SUPER-A-STABLE MOTION WITH BRANCHING O F INDEX 1 + /3 410
2 DICHOTOMY OF STATES AT FIXED TIMES 411
3 ABSOLUTELY CONTINUOUS STATES 411
3.1 DICHOTOMY OF DENSITY FUNCTIONS 411
3.2 LOCAL HOLDER CONTINUITY O F CONTINUOUS DENSITY FUNCTIONS 412
3.3 SOME TRANSITION CURIOSITY 413
3.4 HOLDER CONTINUITY AT A GIVEN POINT 413
3.5 SOME OPEN PROBLEMS 415
4 MAIN TOOLS TO GET THE HDLDER STATEMENTS 417
REFERENCES 421
PART IV MISCELLANEOUS TOPICS IN STATISTICAL MECHANICS
A QUENCHED LARGE DEVIATION PRINCIPLE AND A PARISI FORMULA FOR A
PERCEPTRON VERSION O F THE GREM 425
ERWIN BOLTHAUSEN AND NICOLA KISTLER 1 INTRODUCTION 425
2 A PERCEPTRON VERSION O F THE GREM 426
3 PROOFS 430
3.1 THE GIBBS VARIATIONAL PRINCIPLE: PROOF O F THEOREM 2.3 430
3.2 THE DUAL REPRESENTATION. PROOF O F THE THEOREM 2.5 438
REFERENCES 442
METASTABILITY: FROM MEAN FIELD MODELS TO SPDES 443
ANTON BOVIER 1 INTRODUCTION 443
1.1 STOCHASTIC ISING MODELS 444
2 THE CURIE-WEISS MODEL 445
IMAGE 8
XVIII
C O N T E N T S
3 LARGE DEVIATIONS 447
3.1 DIFFUSIONS WITH SMALL DIFFUSIVITY 448
3.2 JUMP PROCESSES UNDER RESCALING 448
3.3 MARKOV PROCESSES WITH EXPONENTIALLY SMALL TRANSITION PROBABILITIES
449
3.4 LARGE DEVIATIONS BY MASSIVE ENTROPY PRODUCTION 449
4 LIMITATIONS O F THE LARGE DEVIATION APPROACH AND ALTERNATIVES 450
5 CAPACITY ESTIMATES 452
5.1 RANDOM PATH REPRESENTATION AND LOWER BOUNDS ON CAPACITIES 454 5.2
CAPACITY ESTIMATES FOR MESOSCOPIC CHAINS AND THE RETURN O F D = 1 456
6 STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS 458
7 OPEN ISSUES 459
7.1 INITIAL DISTRIBUTIONS AND REGULARITY THEORY 460
7.2 CANONICAL CONSTRUCTIONS O F FLOWS 460
REFERENCES 461
HYDRODYNAMIC LIMIT FOR THE V P INTERFACE MODEL VIA TWO-SCALE APPROACH
463
TADAHISA FUNAKI 1 INTRODUCTION 463
1.1 SETTING 464
1.2 THE GINZBURG-LANDAU V P INTERFACE MODEL 465
1.3 MAIN RESULT 466
2 A PRIORI ESTIMATES 469
3 PROOF OF THEOREM 1.1 470
3.1 DERIVATIVE O F &{T) 471
3.2 THE TERM H 471
3.3 THE TERM L 473
3.4 SUMMARY AND COMPLETION OF THE PROOF OF THEOREM 1.1 479
4 VALIDITY O F ASSUMPTION A FOR CONVEX POTENTIALS 479
4.1 ASSUMPTION A-(2) 479
4.2 ASSUMPTION A-(L) 480
REFERENCES 489
STATISTICAL MECHANICS ON ISORADIAL GRAPHS 491
CEDRIC BOUTILLIER AND BEATRICE DE TILIERE 1 INTRODUCTION 491
1.1 TRANSFER MATRICES, STAR TRANSFORMATIONS, AND Z-INVARIANCE 493
1.2 CONFORMAL FIELD THEORY AND DISCRETE COMPLEX ANALYSIS 495
2 DISCRETE COMPLEX ANALYSIS ON ISORADIAL GRAPHS 495
2.1 DISCRETE HOLOMORPHIC AND DISCRETE HARMONIC FUNCTIONS 495
2.2 DISCRETE EXPONENTIAL FUNCTIONS 497
2.3 GEOMETRIC INTEGRABILITY O F DISCRETE CAUCHY-RIEMANN EQUATIONS - 498
2.4 GENERALIZATION OF THE OPERATOR 3 498
IMAGE 9
CONTENTS X I X
3 DIMER MODEL 499
3.1 DIRAC OPERATOR AND ITS INVERSE 501
3.2 DIRAC OPERATOR AND DIMER MODEL 502
3.3 OTHER RESULTS 503
4 ISING MODEL 504
4.1 CONFORMAL INVARIANCE 505
4.2 THE TWO-DIMENSIONAL ISING MODEL AS A DIMER MODEL 507
5 OTHER MODELS 508
5.1 RANDOM WALK AND THE GREEN FUNCTION 508
5.2 G-POTTS MODELS AND THE RANDOM CLUSTER MODEL 509
5.3 6-VERTEX AND 8-VERTEX MODELS 510
REFERENCES 510
|
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| building | Verbundindex |
| bvnumber | BV041213806 |
| ctrlnum | (OCoLC)811251140 (DE-599)DNB1014072530 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV041213806 |
| illustrated | Illustrated |
| indexdate | 2024-12-24T03:33:00Z |
| institution | BVB |
| isbn | 3642238106 9783642238109 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026188480 |
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| physical | XIX, 512 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| series | Springer proceedings in mathematics |
| series2 | Springer proceedings in mathematics |
| spellingShingle | Probability in complex physical systems in honour of Erwin Bolthausen and Jürgen Gärtner Springer proceedings in mathematics Anderson-Modell (DE-588)4120888-2 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4120888-2 (DE-588)4057630-9 (DE-588)4057000-9 (DE-588)4143413-4 (DE-588)4016928-5 |
| title | Probability in complex physical systems in honour of Erwin Bolthausen and Jürgen Gärtner |
| title_auth | Probability in complex physical systems in honour of Erwin Bolthausen and Jürgen Gärtner |
| title_exact_search | Probability in complex physical systems in honour of Erwin Bolthausen and Jürgen Gärtner |
| title_full | Probability in complex physical systems in honour of Erwin Bolthausen and Jürgen Gärtner Jean-Dominique Deuschel ... ed. |
| title_fullStr | Probability in complex physical systems in honour of Erwin Bolthausen and Jürgen Gärtner Jean-Dominique Deuschel ... ed. |
| title_full_unstemmed | Probability in complex physical systems in honour of Erwin Bolthausen and Jürgen Gärtner Jean-Dominique Deuschel ... ed. |
| title_short | Probability in complex physical systems |
| title_sort | probability in complex physical systems in honour of erwin bolthausen and jurgen gartner |
| title_sub | in honour of Erwin Bolthausen and Jürgen Gärtner |
| topic | Anderson-Modell (DE-588)4120888-2 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Anderson-Modell Stochastischer Prozess Statistische Physik Aufsatzsammlung Festschrift |
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