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Probability Contributions to Statistical Mechanics
Edited by: R. L. Dobrushin

Advances in Soviet Mathematics
1994; 289 pp; hardcover
Volume: 20
ISBN-10: 0-8218-4120-3
ISBN-13: 978-0-8218-4120-4
List Price: US$122
Member Price: US$97.60
Order Code: ADVSOV/20
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Physics has always been a fertile source of new mathematical notions and ideas, and in the past decade the stream of ideas from physics to mathematics has increased dramatically. The subfield of statistical mechanics is no exception. Containing papers written by representatives of the Moscow school of mathematical statistical mechanics, this volume illustrates certain aspects of the developing interaction between statistical mechanics on the one hand and the theories of probability and of dynamical systems on the other. Included here are papers on random walks, phase transition phenomena for Gibbs random fields, the existence of nonstandard motion integrals in statistical physics models, and the Frenkel-Kontorova model.


Graduate students and researchers in mathematics and statistical physics.

Table of Contents

  • J. Abdullaev and R. A. Minlos -- An extension of the Ising model
  • C. Boldrighini, R. A. Minlos, and A. Pellegrinotti -- Central limit theorem for the random walk of one and two particles in a random environment, with mutual interaction
  • R. A. Minlos -- Random walk of a particle interacting with a random field
  • R. L. Dobrushin and S. B. Shlosman -- Large and moderate deviations in the Ising model
  • B. M. Gurevich -- Asymptotically additive integrals of motion for particles with nonpairwise interaction in dimension one
  • L. D. Pustyl'nikov -- On a ground state in the Frenkel-Kontorova model and metric properties of mappings of standard type
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