The Curie-Weiss Model of SOC in Higher Dimension

2015/10/17 by Matthias Gorny, Gorny, Matthias
Mathematics · Physics and Astronomy · #60F05 60K35 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.MP #math.PR #msc:60F05 #msc:60K35

paper · pdf · doi:10.48550/arxiv.1510.05147

arxiv created 2015/10/27 · arxiv updated 2015/10/28

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.

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