Weighted dependency graphs and the Ising model
Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 4, pp. 533-571.
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Weighted dependency graphs have been recently introduced by the second author, as a toolbox to prove central limit theorems. In this paper, we prove that spins in the d-dimensional Ising model display such a weighted dependency structure. We use this to obtain various central limit theorems for the number of occurrences of local and global patterns in a growing box.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/78
Classification : 82-XX, 60-XX
Mots-clés : Ising model, cumulants, central limit theorems, cluster expansions, weighted dependency graphs 
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     author = {Dousse, Jehanne and F\'eray, Valentin},
     title = {Weighted dependency graphs and the {Ising} model},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {533--571},
     volume = {6},
     number = {4},
     year = {2019},
     doi = {10.4171/aihpd/78},
     mrnumber = {4033680},
     zbl = {1447.82006},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/aihpd/78/}
}
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Dousse, Jehanne; Féray, Valentin. Weighted dependency graphs and the Ising model. Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 4, pp. 533-571. doi : 10.4171/aihpd/78. http://www.numdam.org/articles/10.4171/aihpd/78/

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