Weighted dependency graphs and the Ising model
Probability
2017-06-28 v3 Mathematical Physics
Combinatorics
math.MP
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.
Keywords
Cite
@article{arxiv.1610.05082,
title = {Weighted dependency graphs and the Ising model},
author = {Jehanne Dousse and Valentin Féray},
journal= {arXiv preprint arXiv:1610.05082},
year = {2017}
}
Comments
24 pages, 1 figure, version 2 contains new results