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Particle Systems, Random Media and Large Deviations

Edited by: Richard Durrett
Available Formats:
Electronic ISBN: 978-0-8218-7626-8
Product Code: CONM/41.E
List Price: $56.00 MAA Member Price:$50.40
AMS Member Price: $44.80 Click above image for expanded view Particle Systems, Random Media and Large Deviations Edited by: Richard Durrett Available Formats:  Electronic ISBN: 978-0-8218-7626-8 Product Code: CONM/41.E  List Price:$56.00 MAA Member Price: $50.40 AMS Member Price:$44.80
• Book Details

Contemporary Mathematics
Volume: 411985; 380 pp
MSC: Primary 60; Secondary 82;

This volume of proceedings of the 1984 AMS Summer Research Conference The Mathematics of Phase Transitions provides a handy summary of results from some of the most exciting areas in probability theory today: interacting particle systems, percolation, random media (bulk properties and hydrodynamics), the Ising model and large deviations. Thirty-seven mathematicians, many of them well-known probabilists, collaborated to produce this readable introduction to the main results and unsolved problems in the field. In fact, it is one of the very few collections of articles yet to be published on these topics. To appreciate many of the articles, an undergraduate course in probability is sufficient. The book will be valuable to probabilists, especially those interested in mathematical physics and to physicists interested in statistical mechanics or disordered systems.

• Table of Contents

• Articles
• Massimo Campanino - Inequalities for critical probabilities in percolation [ MR 814699 ]
• J. T. Chayes and L. Chayes - Random tubes as a model of pair correlations [ MR 814700 ]
• J. Theodore Cox and David Griffeath - Large deviations for some infinite particle system occupation times [ MR 814701 ]
• Donald A. Dawson and Kenneth J. Hochberg - Function-valued duals for measure-valued processes and applications [ MR 814702 ]
• A. De Masi, P. A. Ferrari, S. Goldstein and W. D. Wick - Invariance principle for reversible Markov processes with application to diffusion in the percolation regime [ MR 814703 ]
• R. Durrett - Stochastic growth models: ten problems for the 80s (and 90s) [ MR 814704 ]
• Richard S. Ellis - Large deviations and statistical mechanics [ MR 814705 ]
• Péter Gács - Nonergodic one-dimensional media and reliable computation [ MR 814706 ]
• H.-O. Georgii - Disordered Ising ferromagnets and percolation [ MR 814707 ]
• Lawrence Gray - The critical behavior of a class of simple interacting systems—a few answers and a lot of questions [ MR 814708 ]
• Andreas Greven - Phase transition for a class of Markov processes on $({\bf N})^S$ [ MR 814709 ]
• Geoffrey Grimmett - Large deviations in subadditive processes and first-passage percolation [ MR 814710 ]
• M. Z. Guo and G. Papanicolaou - Random media and self-diffusion of interacting particles [ MR 814711 ]
• Yasunari Higuchi - A weak version of RSW theorem for the two-dimensional Ising model [ MR 814712 ]
• Richard Holley - Possible rates of convergence in finite range, attractive spin systems [ MR 814713 ]
• Harry Kesten - First-passage percolation and a higher-dimensional generalization [ MR 814714 ]
• Eric S. Key - Using random matrices to give recurrence and transience criteria for random walk in a random environment [ MR 814715 ]
• C. Kipnis - Recent results on the movement of a tagged particle in simple exclusion [ MR 814716 ]
• Shinichi Kotani - On an inverse problem for random Schrödinger operators [ MR 814717 ]
• Gregory F. Lawler - Intersections of simple random walks [ MR 814718 ]
• Neal Madras - A process in a randomly fluctuating environment [ MR 814719 ]
• C. M. Newman and L. S. Schulman - Infinite chains and clusters in one-dimensional directed and undirected percolation [ MR 814720 ]
• Steven Orey - On the Shannon-Perez-Moy theorem [ MR 814721 ]
• Hermann Rost and Maria Eulália Vares - Hydrodynamics of a one-dimensional nearest neighbor model [ MR 814722 ]
• Carolyn L. Schroeder - Decay rates of Green’s functions for the Schrödinger operator [ MR 814723 ]
• Scott Schumacher - Diffusions with random coefficients [ MR 814724 ]
• J. van den Berg - Disjoint occurrences of events: results and conjectures [ MR 814725 ]
• John C. Wierman - Duality for directed site percolation [ MR 814726 ]
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 411985; 380 pp
MSC: Primary 60; Secondary 82;

This volume of proceedings of the 1984 AMS Summer Research Conference The Mathematics of Phase Transitions provides a handy summary of results from some of the most exciting areas in probability theory today: interacting particle systems, percolation, random media (bulk properties and hydrodynamics), the Ising model and large deviations. Thirty-seven mathematicians, many of them well-known probabilists, collaborated to produce this readable introduction to the main results and unsolved problems in the field. In fact, it is one of the very few collections of articles yet to be published on these topics. To appreciate many of the articles, an undergraduate course in probability is sufficient. The book will be valuable to probabilists, especially those interested in mathematical physics and to physicists interested in statistical mechanics or disordered systems.

• Articles
• Massimo Campanino - Inequalities for critical probabilities in percolation [ MR 814699 ]
• J. T. Chayes and L. Chayes - Random tubes as a model of pair correlations [ MR 814700 ]
• J. Theodore Cox and David Griffeath - Large deviations for some infinite particle system occupation times [ MR 814701 ]
• Donald A. Dawson and Kenneth J. Hochberg - Function-valued duals for measure-valued processes and applications [ MR 814702 ]
• A. De Masi, P. A. Ferrari, S. Goldstein and W. D. Wick - Invariance principle for reversible Markov processes with application to diffusion in the percolation regime [ MR 814703 ]
• R. Durrett - Stochastic growth models: ten problems for the 80s (and 90s) [ MR 814704 ]
• Richard S. Ellis - Large deviations and statistical mechanics [ MR 814705 ]
• Péter Gács - Nonergodic one-dimensional media and reliable computation [ MR 814706 ]
• H.-O. Georgii - Disordered Ising ferromagnets and percolation [ MR 814707 ]
• Lawrence Gray - The critical behavior of a class of simple interacting systems—a few answers and a lot of questions [ MR 814708 ]
• Andreas Greven - Phase transition for a class of Markov processes on $({\bf N})^S$ [ MR 814709 ]
• Geoffrey Grimmett - Large deviations in subadditive processes and first-passage percolation [ MR 814710 ]
• M. Z. Guo and G. Papanicolaou - Random media and self-diffusion of interacting particles [ MR 814711 ]
• Yasunari Higuchi - A weak version of RSW theorem for the two-dimensional Ising model [ MR 814712 ]
• Richard Holley - Possible rates of convergence in finite range, attractive spin systems [ MR 814713 ]
• Harry Kesten - First-passage percolation and a higher-dimensional generalization [ MR 814714 ]
• Eric S. Key - Using random matrices to give recurrence and transience criteria for random walk in a random environment [ MR 814715 ]
• C. Kipnis - Recent results on the movement of a tagged particle in simple exclusion [ MR 814716 ]
• Shinichi Kotani - On an inverse problem for random Schrödinger operators [ MR 814717 ]
• Gregory F. Lawler - Intersections of simple random walks [ MR 814718 ]
• Neal Madras - A process in a randomly fluctuating environment [ MR 814719 ]
• C. M. Newman and L. S. Schulman - Infinite chains and clusters in one-dimensional directed and undirected percolation [ MR 814720 ]
• Steven Orey - On the Shannon-Perez-Moy theorem [ MR 814721 ]
• Hermann Rost and Maria Eulália Vares - Hydrodynamics of a one-dimensional nearest neighbor model [ MR 814722 ]
• Carolyn L. Schroeder - Decay rates of Green’s functions for the Schrödinger operator [ MR 814723 ]
• Scott Schumacher - Diffusions with random coefficients [ MR 814724 ]
• J. van den Berg - Disjoint occurrences of events: results and conjectures [ MR 814725 ]
• John C. Wierman - Duality for directed site percolation [ MR 814726 ]
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.