The Curie-Weiss Model of SOC in Higher Dimension

TL;DR

This paper extends the Curie-Weiss model of self-organized criticality to higher dimensions, demonstrating typical critical behavior with specific fluctuation scaling and a novel limiting distribution.

Contribution

It introduces a multidimensional version of the Curie-Weiss SOC model and characterizes its critical fluctuations and limiting law.

Findings

Fluctuations of the sum are of order n^{3/4}

Limiting distribution has a density proportional to exp of a fourth-degree polynomial

Model exhibits typical critical behavior in higher dimensions

Abstract

We build and study a multidimensional version of the Curie-Weiss model of self-organized criticality we have designed in arXiv:1301.6911. For symmetric distributions satisfying some integrability condition, we prove that the sum $S_n$ of the randoms vectors in the model has a typical critical behaviour. The fluctuations are of order $n^{3/4}$ and the limiting law has a density proportional to the exponential of a fourth-degree polynomial.