The Cramér Condition for the Curie-Weiss Model of SOC

2013/11/12 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.1311.2806

Extension of the results of arXiv:1301.6911

arxiv created 2014/10/07 · arxiv updated 2014/10/08

Abstract

We pursue the study of the Curie-Weiss model of self-organized criticality we designed in arXiv:1301.6911. We extend our results to more general interaction functions and we prove that, for a class of symmetric distributions satisfying a Cramér condition (C) and some integrability hypothesis, the sum S_n 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 k exp(-λx⁴) dx where k and λ are suitable positive constants. In arXiv:1301.6911 we obtained these results only for distributions having an even density.

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