Path-space moderate deviations for a class of Curie-Weiss models with dissipation

TL;DR

This paper studies the moderate deviations in a modified Curie-Weiss model with dissipation, analyzing how different phases and transition rates influence the fluctuations of macroscopic observables.

Contribution

It introduces a general analytic approach to derive path-space moderate deviation principles for a class of dissipative Curie-Weiss models with arbitrary transition rates.

Findings

Moderate deviations depend on the phase of the system.

Behavior of fluctuations is influenced by the choice of transition rates.

Path-space moderate deviation principles are established using viscosity solutions.

Abstract

We modify the Glauber dynamics of the Curie-Weiss model with dissipation in Dai Pra, Fischer, Regoli[2013] by considering arbitrary transition rates and we analyze the phase-portrait as well as the dynamics of moderate fluctuations for macroscopic observables. We obtain path-space moderate deviation principles via a general analytic approach based on the convergence of non-linear generators and uniqueness of viscosity solutions for associated Hamilton-Jacobi equations. The moderate asymptotics depend crucially on the phase we are considering and, moreover, their behavior may be influenced by the choice of the rates.