Large scale limits of interacting stochastic models

Swart, Jan M.; Kotecký, Roman
GA ČR 20-08468S, board n. P201

In interacting stochastic models, simple rules on the local level can give rise to complex behaviour on large scales. A natural way to study this phenomenon is through scaling limits and examination of the corresponding asymptomatic behaviour. Sometimes, randomness is present even at the macroscopic level, motivating the study of random continuum models. In other cases, the fluctuations live on a different scale. For models with time evolution, time must often be rescaled too. We aim to study 15 concrete mathematical problems of varying degree of difficulty (some of them meant as problems for doctoral students) concerning the large-scale behaviour of systems defined by microscopic rules, such as one-dimensional Gibbs measures with infinite state space, branching processes, systems with cooperative branching, Potts and random stirring models, and the dynamical Widom-Rowlinson model.