Contemporary Mathematics 1985; 380 pp; softcover Volume: 41 Reprint/Revision History: reprinted 1990 ISBN10: 0821850423 ISBN13: 9780821850428 List Price: US$53 Member Price: US$42.40 Order Code: CONM/41
 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  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  Functionvalued duals for measurevalued 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 onedimensional media and reliable computation
 H. O. Georgii  Disordered Ising ferromagnets and percolation
 L. Gray  The critical behavior of a class of simple interacting systemsa 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 firstpassage percolation
 M. Z. Guo and G. Papanicolau  Random media and selfdiffusion of interacting particles
 Y. Higuchi  A weak version of the RSW for the twodimensional Ising model
 R. Holley  Possible rates of convergence in finite range, attractive spin systems
 H. Kesten  Firstpassage 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 ShannonPerezMoy theorem
 H. Rost and M. E. Vares  Hydrodynamics of a onedimensional 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
