内容説明
This volume is a collection of 15 research and survey papers written by the speakers from two international conferences held in Japan, The 11th Mathematical Society of Japan International Research Institute's Stochastic Analysis on Large Scale Interacting Systems and Stochastic Analysis and Statistical Mechanics. Topics discussed in the volume cover the hydrodynamic limit, fluctuations, large deviations, spectral gap (Poincare 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.
目次
Large deviations for the asymmetric simple exclusion process by S. R. S. Varadhan Random path representation and sharp correlations asymptotics at high temperatures by M. Campanino, D. Ioffe, and Y. Velenik Spectral gap inequalities in product spaces with conservation laws by P. Caputo Ten explicit criteria of one-dimensional processes by M.-F. Chen Probabilistic analysis of directed polymers in a random environment: a review by F. Comets, T. Shiga, and N. Yoshida Entropy pairs and compensated compactness for weakly asymmetric systems by J. Fritz Large deviations for $\nabla \varphi$ interface model and derivation of free boundary problems by T. Funaki and H. Sakagawa A PDE approach for motion of phase-boundaries by a singular interfacial energy by M.-H. Giga and Y. Giga The Dobrushin-Hryniv theory for the two-dimensional lattice Widom-Rowlinson model by Y. Higuchi, J. Murai, and J. Wang Infinite systems of non-colliding Brownian particles by M. Katori, T. Nagao, and H. Tanemura Diffusive behaviour of the equilibrium fluctuations in the asymmetric exclusion processes by C. Landim, S. Olla, and S. R. S. Varadhan Non-collision and collision properties of Dyson's model in infinite dimension and other stochastic dynamics whose equilibrium states are determinantal random point fields by H. Osada Random point fields associated with Fermion, Boson and other statistics by T. Shirai and Y. Takahashi Levy processes conditioned to stay positive and diffusions in random environments by H. Tanaka Zero-range-exclusion particle systems by K. Uchiyama.
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