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.
Citation
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
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