Dynamical moderate deviations for the Curie-Weiss model

TL;DR

This paper establishes moderate deviation principles for the empirical magnetization trajectory in the Curie-Weiss model, revealing phase-dependent asymptotic behaviors using a novel analytic approach involving Hamilton-Jacobi equations.

Contribution

It introduces a general method based on generator convergence and viscosity solutions to derive moderate deviations in the Curie-Weiss model, accounting for phase-specific effects.

Findings

Moderate deviations depend on the phase of the system.

A new analytic approach using Hamilton-Jacobi equations is developed.

Results apply to the trajectory of empirical magnetization.

Abstract

We derive moderate deviation principles for the trajectory of the empirical magnetization of the standard Curie-Weiss model via a general analytic approach based on convergence of generators and uniqueness of viscosity solutions for associated Hamilton-Jacobi equations. The moderate asymptotics depend crucially on the phase under consideration.