On Dobrushin’s Way. From Probability Theory to Statistical Physics ( American Mathematical Society Translations - Series 2 )

Publication series :American Mathematical Society Translations - Series 2

Author: R. A. Minlos;Senya Shlosman;Yu. M. Suhov  

Publisher: American Mathematical Society‎

Publication year: 2000

E-ISBN: 9781470434090

P-ISBN(Hardback):  9780821821503

Subject: O411.1 Mathematical Methods of Physics

Keyword: 暂无分类

Language: ENG

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On Dobrushin’s Way. From Probability Theory to Statistical Physics

Description

R. Dobrushin worked in several branches of mathematics (probability theory, information theory), but his deepest influence was on mathematical physics. He was one of the founders of the rigorous study of statistical physics. When Dobrushin began working in that direction in the early sixties, only a few people worldwide were thinking along the same lines. Now there is an army of researchers in the field. This collection is devoted to the memory of R. L. Dobrushin. The authors who contributed to this collection knew him quite well and were his colleagues. The title, “On Dobrushin's Way”, is meant to stress the fact that the current development of mathematical physics is evolving along the lines that Dobrushin foresaw. His ideas and methods are extensively employed today. Beyond research papers, this volume contains a short biography. Recollections from his contemporaries and younger colleagues are also included. This short biographical section sketches for readers a bit of Dobrushin's qpersonality.

Chapter

Frontispiece

Title page

Copyright page

Contents

Foreword

A brief biography

The lower spectral branch of the generator of the stochastic dynamics for the classical Heisenberg model

Random walk in a fluctuating random environment with Markov evolution

Ergodicity and exponential convergence of a Glauber+Kawasaki process

The Griffiths singularity random field

Dobrushin’s program on Gibbsianity restoration: Weakly Gibbs and almost Gibbs random fields

Space-time invariant states of the ideal gas with finite number, energy, and entropy density

Hausdorff dimension and pressure in the DLR thermodynamic formalism

Nonsymmetric simple random walks along orbits of ergodic automorphisms

The Cramér transform and large deviations on three-dimensional Lobachevsky space

Thermodynamical limit for symmetric closed queuing networks

Random infinite spin graph evolution

An elementary approach to finite size conditions for the exponential decay of covariances in lattice spin models

Dynamics of Ising spin systems at zero temperature

Peierls argument for the anisotropic Ising model

Contour methods and Pirogov-Sinai theory for continuous spin lattice models

Recollections

Back Cover

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