A Curie–Weiss model of self-organized criticality
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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