Advances in Soviet Mathematics 1994; 289 pp; hardcover Volume: 20 ISBN10: 0821841203 ISBN13: 9780821841204 List Price: US$122 Member Price: US$97.60 Order Code: ADVSOV/20
 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 FrenkelKontorova model. Readership 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 FrenkelKontorova model and metric properties of mappings of standard type
