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Scaling Limits of Interacting Particle Systems : Grundlehren der mathematischen Wissenschaften - Claude Kipnis

Scaling Limits of Interacting Particle Systems

Grundlehren der mathematischen Wissenschaften

Hardcover Published: December 1998
ISBN: 9783540649137
Number Of Pages: 444

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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.

"Das Buch ist nach Meinung des Rezensenten eine gelungene Einfuhrung in ein interessantes Gebiet der modernen Stochastik und mathematischen Physik und stellt einen fest umrissenen Gegenstand umfassend dar, vor allem den analytisch-methodischen Aspekt. ... Die Beweise sind ubersichtlich und gut gegliedert, was das Nachvollziehen der Argumente sehr erleichtert; die didaktische Leistung der Autoren in diesem Punkt ist beeindruckend. Ein sorgfaltig zusammengestelltes Literaturverzeichnis von etwa 400 Titeln schliesst das Buch ab. Ingesamt ein sehr gut geschriebener und nutzlicher Band." DMV Jahresbericht, 103. Band, Heft 3, November 2001

Introductionp. 1
An Introductory Example: Independent Random Walksp. 7
Some Interacting Particle Systemsp. 21
Weak Formulations of Local Equilibriump. 41
Hydrodynamic Equation of Symmetric Simple Exclusion Processesp. 47
An Example of Reversible Gradient System: Symmetric Zero Range Processesp. 67
The Relative Entropy Methodp. 115
Hydrodynamic Limit of Reversible Nongradient Systemsp. 141
Hydrodynamic Limit of Asymmetric Attractive Processesp. 191
Conservation of Local Equilibrium for Attractive Systemsp. 231
Large Deviations from the Hydrodynamic Limitp. 257
Equilibrium Fluctuations of Reversible Dynamicsp. 287
Markov Chains on a Countable Spacep. 311
The Equivalence of Ensembles, Large Deviation Tools and Weak Solutions of Quasi-Linear Differential Equationsp. 349
Nongradient Tools: Spectral Gap and Closed Formsp. 373
Referencesp. 425
Subject Indexp. 441
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540649137
ISBN-10: 3540649131
Series: Grundlehren der mathematischen Wissenschaften
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 444
Published: December 1998
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 2.54
Weight (kg): 0.83