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A Hamilton-Jacobi point of view on mean-field Gibbs-non-Gibbs transitions
2017, Kraaij, Richard C., Redig, Frank, Zuijlen, Willem B. van
We study the loss, recovery, and preservation of differentiability of timedependent 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.