# Path-space moderate deviation principles for the random field Curie-Weiss model

## TL;DR

This paper develops a theoretical framework to analyze the moderate deviation principles for the dynamics of the random field Curie-Weiss model, accounting for the effects of disorder on fluctuations.

## Contribution

It introduces a novel analytic approach based on generator convergence and viscosity solutions to establish path space large deviation principles in a disordered setting.

## Key findings

- Path space large deviation principles are derived for the model.
- Moderate fluctuations depend on the phase and disorder.
- The analysis reveals restrictions on fluctuation scales due to disorder.

## Abstract

We analyze the dynamics of moderate fluctuations for macroscopic observables of the random field Curie Weiss model (i.e., standard Curie-Weiss model embedded in a site dependent, i.i.d. random environment). We obtain path space large deviation principles via a general analytic approach based on convergence of non-linear generators and uniqueness of viscosity solutions for associated Hamilton Jacobi equations. The moderate asymptotics depend crucially on the phase we consider and moreover, the space-time scale range for which fluctuations can be proven is restricted by the addition of the disorder.