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Article Dans Une Revue The Annals of Probability Année : 2016

A Curie–Weiss model of self-organized criticality

Matthias Gorny
  • Fonction : Auteur

Résumé

We try to design a simple model exhibiting self-organized criticality, which is amenable to a rigorous mathematical analysis. To this end, we modify the generalized Ising Curie-Weiss model by implementing an automatic control of the inverse temperature. For a class of symmetric distributions whose density satisfies some integrability conditions, we prove that the sum Sn of the random variables behaves as in the typical critical generalized Ising Curie-Weiss model. The fluctuations are of order n 3/4 and the limiting law is C exp(−λx 4) dx where C and λ are suitable positive constants.
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Dates et versions

hal-03827291 , version 1 (24-10-2022)

Identifiants

Citer

Raphaël Cerf, Matthias Gorny. A Curie–Weiss model of self-organized criticality. The Annals of Probability, 2016, 44 (1), ⟨10.1214/14-AOP978⟩. ⟨hal-03827291⟩
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