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

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.

URI

https://doi.org/10.34657/1799
https://oa.tib.eu/renate/handle/123456789/2019

Citation

Kraaij, R. C., Redig, F., & Zuijlen, W. B. v. (2017). A Hamilton-Jacobi point of view on mean-field Gibbs-non-Gibbs transitions (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2461

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Mathematik
WIAS Preprints

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