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

Francesca Collet, Matthias Gorny, Richard C. Kraaij

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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.

Original languageEnglish
Pages (from-to)765-781
Number of pages17
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume56
Issue number2
DOIs
Publication statusPublished - 2020

Keywords

  • Hamilton-Jacobi equation
  • Interacting particle systems
  • Mean-field interaction
  • Moderate deviations
  • Perturbation theory for Markov processes
  • Self-organized criticality

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