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Hardcover ISBN:  9780821821503 
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Hardcover ISBN:  9780821821503 
Product Code:  TRANS2/198 
List Price:  $175.00 
MAA Member Price:  $157.50 
AMS Member Price:  $140.00 
eBook ISBN:  9781470434090 
Product Code:  TRANS2/198.E 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
Hardcover ISBN:  9780821821503 
eBook ISBN:  9781470434090 
Product Code:  TRANS2/198.B 
List Price:  $340.00 $257.50 
MAA Member Price:  $306.00 $231.75 
AMS Member Price:  $272.00 $206.00 

Book DetailsAmerican Mathematical Society Translations  Series 2Advances in the Mathematical SciencesVolume: 198; 2000; 243 ppMSC: Primary 60; 82
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.
ReadershipGraduate students and research mathematicians interested in probability theory and stochastic processes.

Table of Contents

Chapters

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

Aernout van Enter, Christian Maes and Senya Shlosman — Dobrushin’s program on Gibbsianity restoration: Weakly Gibbs and almost Gibbs random fields

Gregory L. Eyink and Herbert Spohn — Spacetime 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 threedimensional 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 exponential 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

Miloš Zahradník — Contour methods and PirogovSinai 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. Vaserstein, MuFa Chen and S. Shlosman — Recollections


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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.

Chapters

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

Aernout van Enter, Christian Maes and Senya Shlosman — Dobrushin’s program on Gibbsianity restoration: Weakly Gibbs and almost Gibbs random fields

Gregory L. Eyink and Herbert Spohn — Spacetime 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 threedimensional 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 exponential 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

Miloš Zahradník — Contour methods and PirogovSinai 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. Vaserstein, MuFa Chen and S. Shlosman — Recollections