4 years ago

A Hamilton-Jacobi point of view on mean-field Gibbs-non-Gibbs transitions.

Frank Redig, Richard C. Kraaij, Willem B. van Zuijlen

We study the loss, recovery, and preservation of differentiability of time-dependent large deviation rate functions. This study is motivated by mean-field Gibbs-non-Gibbs transitions. The gradient of the rate-function evolves according to a Hamiltonian flow. This Hamiltonian flow is used to analyze the regularity of the time dependent rate function, both for Glauber dynamics for the Curie-Weiss model and Brownian dynamics in a potential. We hereby create a unifying framework for the treatment of mean-field Gibbs-non-Gibbs transitions, based on Hamiltonian dynamics and viscosity solutions of Hamilton-Jacobi equations.

Publisher URL: http://arxiv.org/abs/1711.03489

DOI: arXiv:1711.03489v1

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