Gibbs-non-Gibbs transitions via large deviations: computable examples

TL;DR

This paper provides explicit, computable examples of Gibbs-non-Gibbs transitions in mean-field systems using large deviation techniques, covering diffusions like Brownian motion and birth-death processes.

Contribution

It introduces new, explicit examples of Gibbs-non-Gibbs transitions for mean-field models using a large deviation framework, expanding understanding of these phenomena.

Findings

Short-time preservation of Gibbsianness in various models

Explicit computation of Gibbs-non-Gibbs transition points

Applicability to diffusions and birth-death processes

Abstract

We give new and explicitly computable examples of Gibbs-non-Gibbs transitions of mean-field type, using the large deviation approach introduced in [4]. These examples include Brownian motion with small variance and related diffusion processes, such as the Ornstein-Uhlenbeck process, as well as birth and death processes. We show for a large class of initial measures and diffusive dynamics both short-time conservation of Gibbsianness and dynamical Gibbs-non-Gibbs transitions.