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Particle Systems, Random Media and Large Deviations
Edited by: Richard Durrett

Contemporary Mathematics
1985; 380 pp; softcover
Volume: 41
Reprint/Revision History:
reprinted 1990
ISBN-10: 0-8218-5042-3
ISBN-13: 978-0-8218-5042-8
List Price: US$56
Member Price: US$44.80
Order Code: CONM/41
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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. 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

  • M. Campanino -- Inequalities for critical probabilities in percolation
  • J. Chayes and L. Chayes -- Random tubes as a model of pair correlations
  • J. T. Cox and D. Griffeath -- Large deviations for some infinite particle system occupation times
  • D. A. Dawson and K. J. Hochberg -- Function-valued duals for measure-valued processes and applications
  • 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
  • R. Durrett -- Stochastic growth models: Ten problems for the 80's (and 90's)
  • R. S. Ellis -- Large deviations and statistical mechanics
  • P. Gács -- Nonergodic one-dimensional media and reliable computation
  • H. O. Georgii -- Disordered Ising ferromagnets and percolation
  • L. Gray -- The critical behavior of a class of simple interacting systems--a few answers and a lot of questions
  • A. Greven -- Phase transition for a class of Markov processes on \((\mathbb{N})^S\)
  • G. Grimmett -- Large deviations in subadditive processes and first-passage percolation
  • M. Z. Guo and G. Papanicolau -- Random media and selfdiffusion of interacting particles
  • Y. Higuchi -- A weak version of the RSW for the two-dimensional Ising model
  • R. Holley -- Possible rates of convergence in finite range, attractive spin systems
  • H. Kesten -- First-passage percolation and a higher dimensional generalization
  • E. S. Key -- Using random matrices to give recurrence and trancience criteria for random walk in a random environment
  • C. Kipnis -- Recent results on the movement of a tagged particle in simple exclusion
  • S. Kotani -- On the inverse problem for random Schrödinger operators
  • G. F. Lawler -- Intersections of simple random walks
  • N. Madras -- A process in a randomly fluctuating environment
  • C. M. Newman and L. S. Schulman -- Infinite chains and clusters in one dimensional directed and undirected percolation
  • S. Orey -- On the Shannon-Perez-Moy theorem
  • H. Rost and M. E. Vares -- Hydrodynamics of a one-dimensional nearest neighbor model
  • C. L. Schroeder -- Decay rates of Green's functions for the Schrödinger operator
  • S. Schumacher -- Diffusions with random coefficients
  • J. van den Berg -- Disjoint occurrences of events: Results and conjectures
  • J. C. Wierman -- Duality for directed site percolation
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