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Advances in the Mathematical Sciences
On Dobrushin's Way. From Probability Theory to Statistical Physics
Edited by: R. A. Minlos, Russian Academy of Sciences, Moscow, Russia, Senya Shlosman, CPT/CNRS, Marseille, France, and Yu. M. Suhov, Russian Academy of Sciences, Moscow, Russia

American Mathematical Society Translations--Series 2
Advances in the Mathematical Sciences
2000; 243 pp; hardcover
Volume: 198
ISBN-10: 0-8218-2150-4
ISBN-13: 978-0-8218-2150-3
List Price: US$120
Member Price: US$96
Order Code: TRANS2/198
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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.


Graduate students and research mathematicians interested in probability theory and stochastic processes.

Table of Contents

  • N. Angelescu, R. A. Minlos, and V. A. Zagrebnov -- The lower spectral branch of the generator of the stochastic dynamics for the classical Heisenberg model
  • C. Boldrighini, R. A. Minlos, and A. Pellegrinotti -- Random walk in a fluctuating random environment with Markov evolution
  • S. Brassesco, E. Presutti, V. Sidoravicius, and M. E. Vares -- Ergodicity and exponential convergence of a Glauber+Kawasaki process
  • A. van Enter, C. Maes, R. H. Schonmann, and S. Shlosman -- The Griffiths singularity random field
  • A. van Enter, C. Maes, and S. Shlosman -- Dobrushin's program on Gibbsianity restoration: Weakly Gibbs and almost Gibbs random fields
  • G. L. Eyink and H. Spohn -- Space-time invariant states of the ideal gas with finite number, energy, and entropy density
  • B. M. Gurevich and A. A. Tempelman -- Hausdorff dimension and pressure in the DLR thermodynamic formalism
  • V. Yu. Kaloshin and Ya. G. Sinai -- Nonsymmetric simple random walks along orbits of ergodic automorphisms
  • F. I. Karpelevich, E. A. Pechersky, and Yu. M. Suhov -- The Cramér transform and large deviations on three-dimensional Lobachevsky space
  • F. I. Karpelevich and A. N. Rybko -- Thermodynamical limit for symmetric closed queuing networks
  • V. A. Malyshev -- Random infinite spin graph evolution
  • F. Martinelli -- An elementary approach to finite size conditions for the decay of covariances in lattice spin models
  • S. Nanda, C. M. Newman, and D. L. Stein -- Dynamics of Ising spin systems at zero temperature
  • S. A. Pirogov -- Peierls argument for the anisotropic Ising model
  • M. Zahradník -- Contour methods and Pirogov-Sinai theory for continuous spin lattice models
  • R. Minlos, A. M. Vershik, N. D. Vvedenskaya, Yu. D. Apresyan, S. Gindikin, V. M. Tikhomirov, Yu. Suhov, L. N. Vaserstein, M.-F. Chen, and S. Shlosman -- Recollections
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