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 language | English |
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Pages (from-to) | 5287-5329 |
Number of pages | 43 |
Journal | Transactions of the American Mathematical Society |
Volume | 374 |
Issue number | 8 |
DOIs | |
Publication status | Published - 2021 |
Keywords
- Dynamical transition
- Gibbs versus non-Gibbs
- Global minimisers of rate functions
- Hamilton-Jacobi equation
- Hamiltonian dynamics
- Large deviation principle
- Mean-field models