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Weighted dependency graphs and the Ising model


Dousse, Jehanne; Féray, Valentin (2019). Weighted dependency graphs and the Ising model. Annales de l'Institut Henri Poincare D, 6(4):533-571.

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.

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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Additional indexing

Item Type:Journal Article, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistical and Nonlinear Physics
Physical Sciences > Algebra and Number Theory
Physical Sciences > Statistics and Probability
Physical Sciences > Geometry and Topology
Physical Sciences > Discrete Mathematics and Combinatorics
Language:English
Date:4 September 2019
Deposited On:23 Jan 2020 13:10
Last Modified:20 Apr 2022 08:46
Publisher:European Mathematical Society Publishing House
ISSN:2308-5827
OA Status:Green
Publisher DOI:https://doi.org/10.4171/aihpd/78

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