A Curie-Weiss model of self-organized criticality

Abstract

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 $S_n$ 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 $C\exp (-\lambda x^4)dx$ where $C$ and $\lambda$ are suitable positive constants.

Published at http://dx.doi.org/10.1214/14-AOP978 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• A Curie-Weiss Model of Self-Organized Criticality : The Gaussian Case

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