This volume is a collection research and survey papers written by the speakers from two international conferences held in Japan: 1) The 11th Mathematical Society of Japan International Research Institute on Stochastic Analysis on Large Scale Interacting Systems and 2) Stochastic Analysis and Statistical Mechanics.

Topics discussed in the volume cover the hydrodynamic limit, fluctuations, large deviations, spectral gap (Poincaré inequality), logarithmic Sobolev inequality, Ornstein-Zernike asymptotics, random environments, determinantal expressions for systems including exclusion processes (stochastic lattice gas, Kawasaki dynamics), zero range processes, interacting Brownian particles, random walks, self-avoiding walks, Ginzburg-Landau model, interface models, Ising model, Widom-Rowlinson model, directed polymers, random matrices, Dyson's model, and more.

The material is suitable for graduate students and researchers interested in probability theory, stochastic processes, and statistical mechanics.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.

Readership

Graduate students and researchers interested in probability theory, stochastic processes, and statistical mechanics.

Table of Contents

• S. R. S. Varadhan -- Large deviations for the asymmetric simple exclusion process
• M. Campanino, D. Ioffe, and Y. Velenik -- Random path representation and sharp correlations asymptotics at high temperatures
• P. Caputo -- Spectral gap inequalities in product spaces with conservation laws
• M.-F. Chen -- Ten explicit criteria of one-dimensional processes
• F. Comets, T. Shiga, and N. Yoshida -- Probabilistic analysis of directed polymers in a random environment: a review
• J. Fritz -- Entropy pairs and compensated compactness for weakly asymmetric systems
• T. Funaki and H. Sakagawa -- Large deviations for $\nabla \varphi$ interface model and derivation of free boundary problems
• M.-H. Giga and Y. Giga -- A PDE approach for motion of phase-boundaries by a singular interfacial energy
• Y. Higuchi, J. Murai, and J. Wang -- The Dobrushin-Hryniv theory for the two-dimensional lattice Widom-Rowlinson model
• M. Katori, T. Nagao, and H. Tanemura -- Infinite systems of non-colliding Brownian particles
• C. Landim, S. Olla, and S. R. S. Varadhan -- Diffusive behaviour of the equilibrium fluctuations in the asymmetric exclusion processes
• H. Osada -- Non-collision and collision properties of Dyson's model in infinite dimension and other stochastic dynamics whose equilibrium states are determinantal random point fields
• T. Shirai and Y. Takahashi -- Random point fields associated with Fermion, Boson and other statistics
• H. Tanaka -- Lévy processes conditioned to stay positive and diffusions in random environments
• K. Uchiyama -- Zero-range-exclusion particle systems