**American Mathematical Society Translations - Series 2
Advances in the Mathematical Sciences**

2000; 243 pp; Hardcover

MSC: Primary 60; 82;

Print ISBN: 978-0-8218-2150-3

Product Code: TRANS2/198

Print ISBN: 978-0-8218-2150-3

Product Code: TRANS2/198

List Price: $120.00

AMS Member Price: $96.00

MAA Member Price: $108.00

**Electronic ISBN: 978-1-4704-3409-0
Product Code: TRANS2/198.E**

List Price: $120.00

AMS Member Price: $96.00

MAA Member Price: $108.00

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

Share this page *Edited by *
*R. A. Minlos; Senya Shlosman; Yu. M. Suhov*

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.

#### Readership

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

# Table of Contents

## On Dobrushin's Way. From Probability Theory to Statistical Physics

- Cover Cover11
- Frontispiece iv5
- Title page v6
- Copyright page vi7
- Contents vii8
- Foreword ix10
- A brief biography xi12
- The lower spectral branch of the generator of the stochastic dynamics for the classical Heisenberg model 114
- Random walk in a fluctuating random environment with Markov evolution 1326
- Ergodicity and exponential convergence of a Glauber+Kawasaki process 3750
- The Griffiths singularity random field 5164
- Dobrushin’s program on Gibbsianity restoration: Weakly Gibbs and almost Gibbs random fields 5972
- Space-time invariant states of the ideal gas with finite number, energy, and entropy density 7184
- Hausdorff dimension and pressure in the DLR thermodynamic formalism 91104
- Nonsymmetric simple random walks along orbits of ergodic automorphisms 109122
- The Cramér transform and large deviations on three-dimensional Lobachevsky space 117130
- Thermodynamical limit for symmetric closed queuing networks 133146
- Random infinite spin graph evolution 157170
- An elementary approach to finite size conditions for the exponential decay of covariances in lattice spin models 169182
- Dynamics of Ising spin systems at zero temperature 183196
- Peierls argument for the anisotropic Ising model 195208
- Contour methods and Pirogov-Sinai theory for continuous spin lattice models 197210
- Recollections 221234
- Back Cover Back Cover1258