Scaling limits of interacting particle systems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1999
|
| Series: | Die Grundlehren der mathematischen Wissenschaften
320 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 442 S. |
| ISBN: | 3540649131 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Introduction 1
1. An Introductory Example: Independent Random Walks 7
1.1 Equilibrium States 7
1.2 Local Equilibrium 11
1.3 Hydrodynamic Equation 13
1.4 Equivalence of Ensembles 17
1.5 Comments and References 18
2. Some Interacting Particle Systems 21
2.1 Some Remarks on the Topology of Nz i and Mi(Nz ) 21
2.2 Simple Exclusion Processes 25
2.3 Zero Range Processes 28
2.4 Generalized Exclusion Processes 35
2.5 Attractive Systems 36
2.6 Zero Range Processes in Infinite Volume 38
3. Weak Formulations of Local Equilibrium 41
4. Hydrodynamic Equation of Symmetric Simple Exclusion
Processes 47
4.1 Topology and Compactness 49
4.2 The Hydrodynamic Equation 55
4.3 Comments and References 62
5. An Example of Reversible Gradient System: Symmetric Zero
Range Processes 67
5.1 The Law of Large Numbers 69
5.2 Entropy Production 79
5.3 Proof of the Replacement Lemma 81
5.4 The One Block Estimate 84
5.5 The Two Blocks Estimate 92
5.6 A L2 Estimate 98
5.7 An Energy Estimate 103
5.8 Comments and References 109
XII Contents
6. The Relative Entropy Method 115
6.1 Weak Conservation of Local Equilibrium 116
6.2 Comments and References 130
7. Hydrodynamic Limit of Reversible Nongradient Systems 141
7.1 Replacing Currents by Gradients 147
7.2 An Integration by Parts Formula 151
7.3 Nongradient Large Deviation Estimates 154
7.4 Central Limit Theorem Variances 161
7.5 The Diffusion Coefficient 171
7.6 Compactness 180
7.7 Comments and References 184
8. Hydrodynamic Limit of Asymmetric Attractive Processes 191
8.1 Young Measures 200
8.2 An Entropy Inequality at Microscopic Level 208
8.3 Law of Large Numbers for the Empirical Measure 218
8.4 Comments and References 221
9. Conservation of Local Equilibrium for Attractive Systems 231
9.1 Replacement Lemma for Attractive Processes 233
9.2 One Block Estimate Without Time Average 235
9.3 Conservation of Local Equilibrium 246
9.4 Comments and References 251
10. Large Deviations from the Hydrodynamic Limit 257
10.1 The Rate Function 260
10.2 Weakly Asymmetric Simple Exclusion Processes 263
10.3 A Superexponential Estimate 266
10.4 Large Deviations Upper Bound 268
10.5 Large Deviations Lower Bound 273
10.6 Comments and References 279
11. Equilibrium Fluctuations of Reversible Dynamics 287
11.1 The Boltzmann Gibbs Principle 292
11.2 The Martingale Problem 297
11.3 Tightness 299
11.4 Generalized Ornstein Uhlenbeck Processes 307
11.5 Comments and References 309
Contents XIII
Appendices
1. Markov Chains on a Countable Space 311
1.1 Discrete Time Markov Chains 311
1.2 Continuous Time Markov Chains 314
1.3 Kolmogorov s Equations, Generators 321
1.4 Invariant Measures, Reversibility and Adjoint Processes 326
1.5 Some Martingales in the Context of Markov Processes 330
1.6 Estimates on the Variance of Additive Functionals of Markov
Processes 332
1.7 The Feynman Kac Formula 334
1.8 Relative Entropy 338
1.9 Entropy and Markov Processes 340
1.10 Dirichlet Form 343
1.11 A Maximal Inequality for Reversible Markov Processes 346
2. The Equivalence of Ensembles, Large Deviation Tools and Weak
Solutions of Quasi Linear Differential Equations 349
2.1 Local Central Limit Theorem and Equivalence of Ensembles ... 349
2.2 On the Local Central Limit Theorem 357
2.3 Remarks on Large Deviations 362
2.4 Weak Solutions of Nonlinear Parabolic Equations 365
2.5 Entropy Solutions of Quasi Linear Hyperbolic Equations 369
3. Nongradient Tools: Spectral Gap and Closed Forms 373
3.1 On the Spectrum of Reversible Markov Processes 375
3.2 Spectral Gap for Generalized Exclusion Processes 378
3.3 Spectral Gap in Dimension d 2 394
3.4 Closed and Exact Forms 398
3.5 Comments and References 419
References 425
Subject Index 441
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:25:39Z |
| institution | BVB |
| isbn | 3540649131 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008358998 |
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| physical | XVI, 442 S. |
| publishDate | 1999 |
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| series | Die Grundlehren der mathematischen Wissenschaften |
| series2 | Die Grundlehren der mathematischen Wissenschaften |
| spelling | Kipnis, Claude 1949-1993 Verfasser (DE-588)120767244 aut Scaling limits of interacting particle systems Claude Kipnis ; Claudio Landim Berlin [u.a.] Springer 1999 XVI, 442 S. txt rdacontent n rdamedia nc rdacarrier Die Grundlehren der mathematischen Wissenschaften 320 Hydrodynamik Markov-Prozess Skalierungsgesetz Mathematik Mathematische Physik Hydrodynamics Mathematics Markov processes Mathematical physics Probabilities Scaling laws (Statistical physics) Skalierungsgesetz (DE-588)4205012-1 gnd rswk-swf Vielteilchensystem (DE-588)4063491-7 gnd rswk-swf Hydrodynamik (DE-588)4026302-2 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Wechselwirkung (DE-588)4064937-4 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf Vielteilchensystem (DE-588)4063491-7 s Wechselwirkung (DE-588)4064937-4 s Hydrodynamik (DE-588)4026302-2 s DE-604 Skalierungsgesetz (DE-588)4205012-1 s Statistische Physik (DE-588)4057000-9 s Markov-Prozess (DE-588)4134948-9 s Landim, Claudio 1965- Verfasser (DE-588)120477815 aut Die Grundlehren der mathematischen Wissenschaften 320 (DE-604)BV000000395 320 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008358998&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kipnis, Claude 1949-1993 Landim, Claudio 1965- Scaling limits of interacting particle systems Die Grundlehren der mathematischen Wissenschaften Hydrodynamik Markov-Prozess Skalierungsgesetz Mathematik Mathematische Physik Hydrodynamics Mathematics Markov processes Mathematical physics Probabilities Scaling laws (Statistical physics) Skalierungsgesetz (DE-588)4205012-1 gnd Vielteilchensystem (DE-588)4063491-7 gnd Hydrodynamik (DE-588)4026302-2 gnd Markov-Prozess (DE-588)4134948-9 gnd Wechselwirkung (DE-588)4064937-4 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4205012-1 (DE-588)4063491-7 (DE-588)4026302-2 (DE-588)4134948-9 (DE-588)4064937-4 (DE-588)4057000-9 |
| title | Scaling limits of interacting particle systems |
| title_auth | Scaling limits of interacting particle systems |
| title_exact_search | Scaling limits of interacting particle systems |
| title_full | Scaling limits of interacting particle systems Claude Kipnis ; Claudio Landim |
| title_fullStr | Scaling limits of interacting particle systems Claude Kipnis ; Claudio Landim |
| title_full_unstemmed | Scaling limits of interacting particle systems Claude Kipnis ; Claudio Landim |
| title_short | Scaling limits of interacting particle systems |
| title_sort | scaling limits of interacting particle systems |
| topic | Hydrodynamik Markov-Prozess Skalierungsgesetz Mathematik Mathematische Physik Hydrodynamics Mathematics Markov processes Mathematical physics Probabilities Scaling laws (Statistical physics) Skalierungsgesetz (DE-588)4205012-1 gnd Vielteilchensystem (DE-588)4063491-7 gnd Hydrodynamik (DE-588)4026302-2 gnd Markov-Prozess (DE-588)4134948-9 gnd Wechselwirkung (DE-588)4064937-4 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Hydrodynamik Markov-Prozess Skalierungsgesetz Mathematik Mathematische Physik Hydrodynamics Mathematics Markov processes Mathematical physics Probabilities Scaling laws (Statistical physics) Vielteilchensystem Wechselwirkung Statistische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008358998&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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