A Self-Interaction Leading to Fluctuations of Order n^5/6

2014/04/30 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.1404.7637

arxiv created 2014/09/15 · arxiv updated 2014/09/16

Abstract

In arXiv:1301.6911, we built and studied a Curie-Weiss model exhibiting self-organized criticality : it is a model with a self-interaction leading to fluctuations of order n^3/4 and a limiting law proportional to exp(-x⁴/12). In this paper we modify our model in order to "kill the term x⁴" and to obtain a self-interaction leading to fluctuations of order n^5/6 and a limiting law C exp(-λx⁶) dx, for suitable positive constants C and λ.

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