eBook ISBN:  9780821876268 
Product Code:  CONM/41.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821876268 
Product Code:  CONM/41.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 41; 1985; 380 ppMSC: 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. Thirtyseven mathematicians, many of them wellknown 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 — Functionvalued duals for measurevalued 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 onedimensional 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 firstpassage percolation [ MR 814710 ]

M. Z. Guo and G. Papanicolaou — Random media and selfdiffusion of interacting particles [ MR 814711 ]

Yasunari Higuchi — A weak version of RSW theorem for the twodimensional Ising model [ MR 814712 ]

Richard Holley — Possible rates of convergence in finite range, attractive spin systems [ MR 814713 ]

Harry Kesten — Firstpassage percolation and a higherdimensional 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 onedimensional directed and undirected percolation [ MR 814720 ]

Steven Orey — On the ShannonPerezMoy theorem [ MR 814721 ]

Hermann Rost and Maria Eulália Vares — Hydrodynamics of a onedimensional 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 ]


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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. Thirtyseven mathematicians, many of them wellknown 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 — Functionvalued duals for measurevalued 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 onedimensional 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 firstpassage percolation [ MR 814710 ]

M. Z. Guo and G. Papanicolaou — Random media and selfdiffusion of interacting particles [ MR 814711 ]

Yasunari Higuchi — A weak version of RSW theorem for the twodimensional Ising model [ MR 814712 ]

Richard Holley — Possible rates of convergence in finite range, attractive spin systems [ MR 814713 ]

Harry Kesten — Firstpassage percolation and a higherdimensional 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 onedimensional directed and undirected percolation [ MR 814720 ]

Steven Orey — On the ShannonPerezMoy theorem [ MR 814721 ]

Hermann Rost and Maria Eulália Vares — Hydrodynamics of a onedimensional 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 ]