Large deviations of mean-field interacting particle systems in a fast varying environment

Abstract

This paper studies large deviations of a "fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment evolves in the fast time scale. Our main result is the path-space large deviation principle for the joint law of the empirical measure process of the particles and the occupation measure process of the fast environment. This extends previous results known for two time scale diffusions to two time scale mean-field models with jumps. Our proof is based on the method of stochastic exponentials. We characterise the rate function by studying a certain variational problem associated with an exponential martingale.

Active gating: rocking diffusion channels

“…Similar models and ideas have appeared in other contexts, e.g. in [7,8] for mathematical aspects. On the experimental side, the models appear related to the bio-and chemical physics in e.g.…”

Active gating: rocking diffusion channels

“…Similar models and ideas have appeared in other contexts, e.g. in [6,7] for mathematical aspects. On the experimental side, the models appear related to the bio-and chemical physics in e.g.…”

“…The switching of contacts happens at rate r with entrance rates α, γ and exit rates β, δ. The chemical potentials μ(+) and μ(−) correspond to the reservoirs, respectively above and below the dashed line, see equation (6).…”