Path-space moderate deviations for a Curie-Weiss model of self-organized criticality

TL;DR

This paper establishes a path-space moderate deviation principle for the magnetization in a Curie-Weiss model of self-organized criticality, revealing critical behavior without parameter tuning.

Contribution

It introduces a novel analytic approach to analyze moderate fluctuations in the SOC Curie-Weiss model, deriving a path-space moderate deviation principle.

Findings

Magnetization exhibits critical behavior under specific scaling.

Path-space moderate deviation principle is established.

Analysis is based on convergence of non-linear generators.

Abstract

The dynamical Curie-Weiss model of self-organized criticality (SOC) was introduced in \cite{Gor17} and it is derived from the classical generalized Curie-Weiss by imposing a microscopic Markovian evolution having the distribution of the Curie-Weiss model of SOC [Cerf, Gorny 2016] as unique invariant measure. In the case of Gaussian single-spin distribution, we analyze the dynamics of moderate fluctuations for the magnetization. We obtain a path-space moderate deviation principle via a general analytic approach based on convergence of non-linear generators and uniqueness of viscosity solutions for associated Hamilton-Jacobi equations. Our result shows that, under a peculiar moderate space-time scaling and without tuning external parameters, the typical behavior of the magnetization is critical.