**Contemporary Mathematics**

Volume: 41;
1985;
380 pp;
Softcover

MSC: Primary 60;
Secondary 82

Print ISBN: 978-0-8218-5042-8

Product Code: CONM/41

List Price: $56.00

AMS Member Price: $44.80

MAA member Price: $50.40

**Electronic ISBN: 978-0-8218-7626-8
Product Code: CONM/41.E**

List Price: $56.00

AMS Member Price: $44.80

MAA member Price: $50.40

# Particle Systems, Random Media and Large Deviations

Share this page *Edited by *
*Richard Durrett*

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

## Particle Systems, Random Media and Large Deviations

- Table of Contents vii8 free
- Introduction ix10 free
- Inequalities for critical probabilities in percolation 112 free
- Random tubes as a model of pair correlations 1122
- Large deviations for some infinite particle system occupation times 4354
- Function-valued duals for measure-valued processes and applications 5566
- Invariance principle for reversible Markov processes with application to diffusion in the percolation regime 7182
- Stochastic growth models: Ten problems for the 80's (and 90's) 8798
- Large deviations and statistical mechanics 101112
- Nonergodic one-dimensional media and reliable computation 125136
- Disordered Ising ferromagnets and percolation 135146
- The critical behavior of a class of simple interacting systems -- a few answers and a lot of questions 149160
- Phase transition for a class of Markov processes on (N)S 161172
- Large deviations in subadditive processes and first-passage percolation 175186
- Random media and selfdiffusion of interacting particles 195206
- A weak version of the RSW for the two-dimensional Ising model 207218
- Possible rates of convergence in finite range, attractive spin systems 215226
- First-passage percolation and a higher dimensional generalization 235246
- Using random matrices to give recurrence and trancience criteria for random walk in a random environment 253264
- Recent results on the movement of a tagged particle in simple exclusion 259270
- On the inverse problem for random Schrödinger operators 267278
- Intersections of simple random walks 281292
- A process in a randomly fluctuating environment 291302
- Infinite chains and clusters in one dimensional directed and undirected percolation 297308
- On the Shannon-Perez-Moy Theorem 319330
- Hydrodynamics of a one-dimensional nearest neighbor model 329340
- Decay rates of Green's functions for the Schrodinger operator 343354
- Diffusions with random coefficients 351362
- Disjoint occurrences of events: Results and conjectures 357368
- Duality for directed site percolation 363374