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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 -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.
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Jehanne Dousse, Valentin Féray, Weighted dependency graphs and the Ising model. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), no. 4, pp. 533–571DOI 10.4171/AIHPD/78