Path-space moderate deviations for a Curie-Weiss model of self-organized criticality
| Autor: | Francesca Collet, Richard C. Kraaij, Matthias Gorny |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Interacting particle systems Self-organized criticality Gaussian Mean-field interaction symbols.namesake Moderate deviations Hamilton–Jacobi equation FOS: Mathematics Statistical physics Uniqueness Scaling 60J60 Mathematics Curie–Weiss law Probability (math.PR) Perturbation theory for Markov processes Hamilton-Jacobi equation 60F10 60K35 Distribution (mathematics) Criticality 60K35 symbols Invariant measure Statistics Probability and Uncertainty Mathematics - Probability 60F10 |
| Zdroj: | Ann. Inst. H. Poincaré Probab. Statist. 56, no. 2 (2020), 765-781 Annales de l'Institut Henri Poincar. (B) Probabilites et Statistiques, 56(2) |
| ISSN: | 0246-0203 |
| Popis: | 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. arXiv admin note: text overlap with arXiv:1705.00988 |
| Databáze: | OpenAIRE |
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