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arXiv · 1610.05082

Weighted dependency graphs and the Ising model

Jehanne Dousse·Valentin Féray
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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 $d$-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.

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Jehanne Dousse, Valentin Féray. 2016-10-17. Weighted dependency graphs and the Ising model. https://arxiv.org/abs/1610.05082

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