Weighted dependency graphs and the Ising model
Jehanne Dousse
Universität Zürich, Switzerland and Université de Lyon, Villeurbanne, FranceValentin Féray
Universität Zürich, Switzerland
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Abstract
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 -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.
Cite this article
Jehanne Dousse, Valentin Féray, Weighted dependency graphs and the Ising model. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), no. 4, pp. 533–571
DOI 10.4171/AIHPD/78