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

Journal article (2020)

Authors

F. Collet Applied Probability - EEMCS , Università degli Studi di Padova
Matthias Gorny Laboratoire de Mathématiques d'Orsay
R.C. Kraaij Applied Probability - EEMCS
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2020 F. Collet, Matthias Gorny, R.C. Kraaij
DOI
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https://doi.org/10.1214/19-AIHP981
Mean-field interaction Self-organized criticality Interacting particle systems Moderate deviations Hamilton-Jacobi equation Perturbation theory for Markov processes
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Published Date

2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

Abstract

The dynamical Curie-Weiss model of self-organized criticality (SOC) was introduced in (Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 658-678) 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 (Ann. Probab. 44 (2016) 444-478) 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.

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