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

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

Collet, F. (TU Delft Applied Probability; Università degli Studi di Padova)
Gorny, Matthias (Laboratoire de Mathématiques d'Orsay)
Kraaij, R.C. (TU Delft Applied Probability)

2020

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.

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

http://resolver.tudelft.nl/uuid:c230fa2a-307c-4667-bd10-43b9708075fd

https://doi.org/10.1214/19-AIHP981

0246-0203

Annales de l'Institut Henri Poincar. (B) Probabilites et Statistiques, 56 (2), 765-781

Institutional Repository

journal article

© 2020 F. Collet, Matthias Gorny, R.C. Kraaij