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Weighted dependency graphs and the Ising model
- Publication Year :
- 2016
-
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.<br />Comment: 24 pages, 1 figure, version 2 contains new results
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1610.05082
- Document Type :
- Working Paper