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The Curie-Weiss Model of SOC in Higher Dimension
Matthias Gorny1
1 Université Paris-Sud and ENS Paris, Paris (France)
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 1, pp. 91-108.

We build and study a multidimensional version of the Curie-Weiss model of self-organized criticality we have designed in [2]. For symmetric distributions satisfying some integrability condition, we prove that the sum S n of the randoms vectors in the model has a typical critical asymptotic behaviour. The fluctuations are of order n 3/4 and the limiting law has a density proportional to the exponential of a fourth-degree polynomial.

Nous construisons et étudions une version multi-dimensionnelle du modèle d’Ising Curie-Weiss de criticalité auto-organisée que nous avons introduit dans [2]. Pour des distributions vérifiant une certaine condition d’intégrabilité, nous montrons que la somme S n des variables aléatoires du modèle a un comportement asymptotique critique typique. Les fluctuations sont d’ordre n 3/4 et la loi limite admet une densité proportionnelle à l’exponentielle d’un polynôme de degré quatre.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1594
Classification: 60F05, 60K35
Keywords: Ising Curie-Weiss, SOC, Laplace’s method

Matthias Gorny 1

1 Université Paris-Sud and ENS Paris, Paris (France)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Matthias Gorny. The Curie-Weiss Model of SOC in Higher Dimension. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 1, pp. 91-108. doi : 10.5802/afst.1594. https://afst.centre-mersenne.org/articles/10.5802/afst.1594/

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