Path-space moderate deviations for a Curie-Weiss model of self-organized criticality
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.
Keywords
Cite
@article{arxiv.1801.08840,
title = {Path-space moderate deviations for a Curie-Weiss model of self-organized criticality},
author = {Francesca Collet and Matthias Gorny and Richard Clemens Kraaij},
journal= {arXiv preprint arXiv:1801.08840},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1705.00988