A Dynamical Curie-Weiss Model of SOC: The Gaussian Case

2015/07/03 by Matthias Gorny, Gorny, Matthias
Mathematics · Physics and Astronomy · #60J60 #60K35 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.MP #math.PR #msc:60J60 #msc:60K35

paper · pdf · doi:10.48550/arxiv.1507.00924

arxiv created 2015/11/15 · arxiv updated 2015/11/17

Abstract

In this paper, we introduce a Markov process whose unique invariant distribution is the Curie-Weiss model of self-organized criticality (SOC) we designed in arXiv:1301.6911. In the Gaussian case, we prove rigorously that it is a dynamical model of SOC: the fluctuations of the sum S_n( ⋅ ) of the process evolve in a time scale of order √(n) and in a space scale of order n^3/4 and the limiting process is the solution of a "critical" stochastic differential equation.

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