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 des variables aléatoires du modèle a un comportement asymptotique critique typique. Les fluctuations sont d’ordre et la loi limite admet une densité proportionnelle à l’exponentielle d’un polynôme de degré quatre.
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 of the randoms vectors in the model has a typical critical asymptotic behaviour. The fluctuations are of order and the limiting law has a density proportional to the exponential of a fourth-degree polynomial.
Accepté le :
Publié le :
DOI : 10.5802/afst.1594
Mots clés : Ising Curie-Weiss, SOC, Laplace’s method
@article{AFST_2019_6_28_1_91_0,
author = {Gorny, Matthias},
title = {The {Curie-Weiss} {Model} of {SOC} in {Higher} {Dimension}},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {91--108},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 28},
number = {1},
year = {2019},
doi = {10.5802/afst.1594},
mrnumber = {3940793},
zbl = {1420.60036},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/afst.1594/}
}
TY - JOUR AU - Gorny, Matthias TI - The Curie-Weiss Model of SOC in Higher Dimension JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2019 SP - 91 EP - 108 VL - 28 IS - 1 PB - Université Paul Sabatier, Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1594/ DO - 10.5802/afst.1594 LA - en ID - AFST_2019_6_28_1_91_0 ER -
%0 Journal Article %A Gorny, Matthias %T The Curie-Weiss Model of SOC in Higher Dimension %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2019 %P 91-108 %V 28 %N 1 %I Université Paul Sabatier, Toulouse %U http://archive.numdam.org/articles/10.5802/afst.1594/ %R 10.5802/afst.1594 %G en %F AFST_2019_6_28_1_91_0
Gorny, Matthias. The Curie-Weiss Model of SOC in Higher Dimension. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 1, pp. 91-108. doi : 10.5802/afst.1594. http://archive.numdam.org/articles/10.5802/afst.1594/
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