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

Journal Article (2020)
Author(s)

Francesca Collet (Università degli Studi di Padova, TU Delft - Applied Probability)

Matthias Gorny (Laboratoire de Mathématiques d'Orsay)

RICHARD C. KRAAIJ (TU Delft - Applied Probability)

Research Group
Applied Probability
Copyright
© 2020 F. Collet, Matthias Gorny, R.C. Kraaij
DOI related publication
https://doi.org/10.1214/19-AIHP981
More Info
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Publication Year
2020
Language
English
Copyright
© 2020 F. Collet, Matthias Gorny, R.C. Kraaij
Research Group
Applied Probability
Issue number
2
Volume number
56
Pages (from-to)
765-781
Reuse Rights

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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.

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