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arXiv · 1306.1561

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

Matthias Gorny
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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 $σ^{2}$, 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 $C \exp(-x^{4}/(4σ^4))\,dx$ where $C$ is a suitable positive constant.

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Matthias Gorny. 2013-06-06. A Curie-Weiss Model of Self-Organized Criticality : The Gaussian Case. https://arxiv.org/abs/1306.1561

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