Scaling Limits of Interacting Particle Systems

Claude Kipnis, Claudio Landim

442 pages, parution le 01/01/1998

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Résumé

This book presents in a progressive way the techniques used in the proof of the hydrodynamic behavior of interacting particle systems. It starts with introductory material on independent particles and goes all the way to nongradient systems, covering the entropy and the relative entropy methods, asymmetric processes from which hyperbolic equations emerge, the equilibrium fluctuations and the large deviations theory for short-range stochastic dynamics. It reviews, in appendices, some tools of Markov process theory and derives estimates on the spectral gap of reversible, conservative generators. The book is self-contained and can be read by graduate students in mathematics or mathematical physics with standard probability background. It can be used as a support for a graduate on stochastic processes.

Contents

Introduction 1

1 An Introductory Example: Independent Random Walks 7
2 Some Interacting Particle Systems 21
3 Weak Formulations of Local Equilibrium 41
4 Hydrodynamic Equation of Symmetric Simple Exclusion Processes 47
5 An Example of Reversible Gradient System: Symmetric Zero Range Processes 67
6 The Relative Entropy Method 115
7 Hydrodynamic Limit of Reversible Nongradient Systems 141
8 Hydrodynamic Limit of Asymmetric Attractive Processes 191
9 Conservation of Local Equilibrium for Attractive Systems 231
10 Large Deviations from the Hydrodynamic Limit 257
11 Equilibrium Fluctuations of Reversible Dynamics 287

App. 1 Markov Chains on a Countable Space 311
App. 2 The Equivalence of Ensembles, Large Deviation Tools and Weak Solutions of Quasi-Linear Differential Equations 349
App. 3 Nongradient Tools: Spectral Gap and Closed Forms 373

References 425
Subject Index 441

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Claude Kipnis, Claudio Landim
Parution	01/01/1998
Nb. de pages	442
Format	16 x 24
Couverture	Relié
Poids	793g
Intérieur	Noir et Blanc
EAN13	9783540649137