WIAS Preprint No. 2461, (2017)

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



Authors

  • Kraaij, Richard
  • Redig, Frank
  • van Zuijlen, Willem

2010 Mathematics Subject Classification

  • 49L99 60F10 82C22 82C27

Keywords

  • Hamiltonian dynamics, Hamilton-Jacobi equation, mean-field models, large deviation principle, Gibbs versus non-Gibbs, dynamical transition, global minimisers of rate functions

DOI

10.20347/WIAS.PREPRINT.2461

Abstract

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.

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