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

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.

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• Critical Fluctuations at Finite-Time Dynamical Phase Transition
• Large deviations of the trajectory of empirical distributions of Feller processes on locally compact spaces
• On the prevalence of non-Gibbsian states in mathematical physics
• A Hamilton-Jacobi point of view on mean-field Gibbs-non-Gibbs transitions
• Hamiltonian and Lagrangian for the trajectory of the empirical distribution and the empirical measure of Markov processes
• Synchronization for discrete mean-field rotators