A hamilton-jacobi point of view on mean-field gibbs-non-gibbs transitions

RICHARD C. KRAAIJ, FRANK REDIG, WILLEM B. VAN ZUIJLEN

Research output: Contribution to journalArticleScientificpeer-review

5 Downloads (Pure)

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 extend the variational approach to this problem of time-dependent regularity in order to include Hamiltonian trajectories with a finite lifetime in closed domains with a boundary. This leads to new phenomena, such a recovery of smoothness. We hereby create a new and unifying approach for the study of mean-field Gibbs-non-Gibbs transitions, based on Hamiltonian dynamics and viscosity solutions of Hamilton-Jacobi equations.

Original languageEnglish
Pages (from-to)5287-5329
Number of pages43
JournalTransactions of the American Mathematical Society
Volume374
Issue number8
DOIs
Publication statusPublished - 2021

Keywords

  • Dynamical transition
  • Gibbs versus non-Gibbs
  • Global minimisers of rate functions
  • Hamilton-Jacobi equation
  • Hamiltonian dynamics
  • Large deviation principle
  • Mean-field models

Fingerprint

Dive into the research topics of 'A hamilton-jacobi point of view on mean-field gibbs-non-gibbs transitions'. Together they form a unique fingerprint.

Cite this