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

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. With the help of exact computations, we show that, in the case of a centered Gaussian measure with positive variance ${\sigma }^2$, the sum $S_n$ of the random variables has fluctuations of order $n^{3/4}$ and that $S_n/n^{3/4}$ converges to the distribution $C\exp (-x^4/(4{\sigma }^4))dx$ where $C$ is a suitable positive constant.

The Gaussian case, initially in the first version of arXiv:1301.6911, removed from the second version and presented here

References in corpus (1)

• A Curie-Weiss model of self-organized criticality

Cited by in corpus (4)

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• Path-space moderate deviations for a Curie-Weiss model of self-organized criticality
• An extension of the Ising-Curie-Weiss model of self-organized criticality with a threshold on the interaction range