A CURIE-WEISS MODEL OF SELF-ORGANIZED CRITICALITY
成果类型：
Article
署名作者：
Cerf, Raphael; Gorny, Matthias
署名单位：
Universite Paris Saclay
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/14-AOP978
发表日期：
2016
页码：
444-478
关键词：
摘要：
We try to design a simple model exhibiting self-organized criticality, which is amenable to a rigorous mathematical analysis. To this end, we modify the generalized Ising Curie-Weiss model by implementing an automatic control of the inverse temperature. For a class of symmetric distributions whose density satisfies some integrability conditions, we prove that 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 C exp(-lambda x(4)) dx where C and lambda are suitable positive constants.