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arXiv · 1801.08840

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

Francesca Collet·Matthias Gorny·Richard Clemens Kraaij
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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.

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Francesca Collet, Matthias Gorny, Richard Clemens Kraaij. 2018-01-26. Path-space moderate deviations for a Curie-Weiss model of self-organized criticality. https://doi.org/10.1214/19-aihp981

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