Quenched large deviations for Glauber evolution with Kac interaction and Random Field

TL;DR

This paper establishes a large deviations principle for the empirical magnetizations of a spin-flip model with Kac interaction and random field, revealing how external randomness influences the system's behavior.

Contribution

It introduces a large deviations framework for Glauber dynamics with Kac interaction in a random field, accounting for spatial inhomogeneity and external randomness.

Findings

Large deviations principle holds almost surely with respect to the random field.

The rate functional depends on the statistical properties of the external random field.

The rate functional is lower semicontinuous with compact level sets.

Abstract

We study a spin-flip model with Kac type interaction, in the presence of a random field given by i.i.d. bounded random variables. The system, spatially inhomogeneous, evolves according to a non conservative (Glauber) dynamics. We show an almost sure (with respect to the random field) large deviations principle for the empirical magnetizations of this process. The rate functional depends on the statistical properties of the external random field, it is lower semicontinuous with compact level sets.