Open Access
August 2016 The Cramér condition for the Curie–Weiss model of SOC
Matthias Gorny
Braz. J. Probab. Stat. 30(3): 401-431 (August 2016). DOI: 10.1214/15-BJPS286


We pursue the study of the Curie–Weiss model of self-organized criticality we designed in (Ann. Probab. 44 (2016) 444–478). 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 $k\exp(-\lambda x^{4})dx$ where $k$ and $\lambda$ are suitable positive constants. In (Ann. Probab. 44 (2016) 444–478), we obtained these results only for distributions having an even density.


Download Citation

Matthias Gorny. "The Cramér condition for the Curie–Weiss model of SOC." Braz. J. Probab. Stat. 30 (3) 401 - 431, August 2016.


Received: 1 October 2014; Accepted: 1 February 2015; Published: August 2016
First available in Project Euclid: 29 July 2016

zbMATH: 1366.60108
MathSciNet: MR3531691
Digital Object Identifier: 10.1214/15-BJPS286

Keywords: Ising Curie–Weiss , Laplace’s method , Self-organized criticality

Rights: Copyright © 2016 Brazilian Statistical Association

Vol.30 • No. 3 • August 2016
Back to Top