Electronic ISBN:  9780821876268 
Product Code:  CONM/41.E 
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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 ]