In and Out of Equilibrium

by Brazilian School of Probability 2000 (Rio De Janeiro, Brazil); Sidoravicius, Vladas

• ISBN13: 9780817642891
• ISBN10: 0817642897
• Format: Hardcover
• Copyright: 2002-05-01
• Publisher: Birkhauser

Summary

The intersection of probability and physics has been a rich and explosive area of growth in the past two decades, specifically covering such subjects as percolation theory, random walks, interacting particle systems, and various topics related to statistical mechanics. In the last several years, substantial progress has been made in a number of directions: fluctuations of 2-dimensional growth processes, Wulf constructions in higher dimensions for percolation, Potts and Ising models, classification of random walks in random environments, the introduction of the stochastic Loewner equation, the rigorous proof of intersection exponents for planar Brownian motion, and finally the proof of conformal invariance for critical percolation on the triangular lattice. This volume consists of a collection of invited articles, written by some of the most distinguished probabilists in the above-mentioned areas, most of whom were personally responsible for advances in the various subfields of probability. All of the articles are an outgrowth of the Fourth Brazilian School of Probability, held in Mambucaba, Brazil, August 2000. Contributors: K. Alexander * J.M. Azaïs * J. van den Berg * T. Bodineau * F. Camia * N. Cancrini * G. Grimmett * P. Hiemer * A.E. Holroyd * H. Kesten * G.F. Lawler * T.M. Liggett * J. Lorinczi * F. Martinelli * C. M. Newman * J. Quastel * C.-E. Pfister * M. Prähofer * C. Roberto * O. Schramm * V. Sidoravicius * H. Spohn * A. Toom * B. Tóth * D. Ueltschi * W. Werner * M. Wschebor * M. Wüthrich Graduate students and researchers in probability theory and math physics will find this book a useful reference.

Table of Contents

Preface
Randomly Coalescing Random Walk in Dimensions [greater than or equal to] 3	p. 1
The Single Droplet Theorem for Random Cluster Models	p. 47
Phase Coexistence for the Kac-Ising Models	p. 75
Sharp Estimates for Brownian Non-intersection Probabilities	p. 113
Tagged Particle Distributions or How to Choose a Head at Random	p. 133
Approach to Fixation for Zero-Temperature Stochastic Ising Models on the Hexagonal Lattice	p. 163
Current Fluctuations for the Totally Asymmetric Simple Exclusion Process	p. 185
Asymptotic Behaviour of Semi-Infinite Geodesics for Maximal Increasing Subsequences in the Plane	p. 205
Hydrodynamic Equation for a Deposition Model	p. 227
Time Reversal of Degenerate Diffusions	p. 249
Spectral Gap and Logarithmic Sobolev Constant of Kawasaki Dynamics Under a Mixing Condition Revisited	p. 259
Directed Percolation and Random Walk	p. 273
Entanglement and Rigidity in Percolation Models	p. 299
On Critical Values for Some Random Processes with Local Interaction in R[superscript 2]	p. 309
The Distribution of the Maximum of a Gaussian Process: Rice Method Revisited	p. 321
Gibbs Measures on Brownian Paths	p. 349
Geometric and Probabilistic Aspects of Boson Lattice Models	p. 363
Thermodynamical Aspects of Classical Lattice Systems	p. 393
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