Dousse, Jehanne; Féray, Valentin (2019). Weighted dependency graphs and the Ising model. Annales de l'Institut Henri Poincare D, 6(4):533-571.
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.
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.
| 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: | 23 Nov 2023 02:44 |
| Publisher: | European Mathematical Society Publishing House |
| ISSN: | 2308-5827 |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.4171/aihpd/78 |
Dousse, Jehanne