Particle Systems, Random Media and Large Deviations

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