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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

Abstract

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.

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

Information

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

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Vol.30 • No. 3 • August 2016
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