The idea of writing up a book on the hydrodynamic behavior of interacting particle systems
was born after a series of lectures Claude Kipnis gave at the University of Paris 7 in the …

Interactive Particle Systems is a branch of Probability Theory with close connections to
Mathematical Physics and Mathematical Biology. In 1985, the author wrote a book (T …

We consider two strictly related models: a solid on solid interface growth model and the
weakly asymmetric exclusion process, both on the one dimensional lattice. It has been …

The present volume contains the most advanced theories on the martingale approach to
central limit theorems. Using the time symmetry properties of the Markov processes, the …

Abstract We consider N× N Hermitian random matrices with independent identical
distributed entries. The matrix is normalized so that the average spacing between …

It is shown that the chaoticity hypothesis recently introduced in statistical mechanics, which
is analogous to Ruelle's principle for turbulence, implies the Onsager reciprocity and the …

We derive hydrodynamic equations for systems not in local thermodynamic equilibrium, that
is, where the local stationary measures are “non-Gibbsian” and do not satisfy detailed …

The addition of stochastic terms to a deterministic equation describing the time evolution of a
macroscopic physical system is often done in a heuristic intuitive way. However for …

The goal of the present paper is to establish a framework which allows to rigorously
determine the large-scale Gaussian fluctuations for a class of singular SPDEs at and above …

The problem of transition from a microscopic description of a system with a large number of
components to the description of a suitably scaled version of the same system by a few …