JournalsaihpdVol. 6, No. 4pp. 533–571

Weighted dependency graphs and the Ising model

  • Jehanne Dousse

    Universität Zürich, Switzerland and Université de Lyon, Villeurbanne, France
  • Valentin 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 dd-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