Large Scale Stochastic Dynamics

Abstract

Equilibrium statistical mechanics studies random fields distributed according to a Gibbs probability measure. Such random fields can be equipped with a stochastic dynamics given by a Markov process with the correspondingly high-dimensional state space. One particular case are stochastic partial differential equations suitably regularized. Another common version is to consider the evolution of random fields taking only values 0 or 1. The workshop was concerned with an understanding of qualitative properties of such high-dimensional Markov processes. Of particular interest are nonreversible dynamics for which the stationary measures are determined only through the dynamics and not given a priori (as would be the case for reversible dynamics). As a general observation, properties on a large scale do not depend on the precise details of the local updating rules. Such kind of universality was a guiding theme of our workshop.