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

Francesca Collet; Matthias Gorny; Richard C. Kraaij

doi:10.1214/19-AIHP981

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

Francesca Collet, Matthias Gorny, Richard C. Kraaij

Applied Probability

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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 language	English
Pages (from-to)	765-781
Number of pages	17
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	56
Issue number	2
DOIs	https://doi.org/10.1214/19-AIHP981
Publication status	Published - 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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10.1214/19-AIHP981

1801.08840Accepted author manuscript, 270 KB

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title = "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 (Ann. Inst. Henri Poincar{\'e} 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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AU - Collet, Francesca

AU - Gorny, Matthias

AU - Kraaij, Richard C.

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Y1 - 2020

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KW - Hamilton-Jacobi equation

KW - Interacting particle systems

KW - Mean-field interaction

KW - Moderate deviations

KW - Perturbation theory for Markov processes

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JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 2

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

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