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Poisson approximation for large-contours in low-temperature Ising models | | Pablo A. Ferrari
; Pierre Picco
; | | Date: |
17 Dec 1999 | | Journal: | Physica A: Statistical Mechanics and its Applications, Volume 279, Issues 1-4, Pages 303-311 | | Subject: | Probability; Mathematical Physics MSC-class: 60K35; 82B; 82C; 60F17; 60F05 | math.PR math-ph math.MP | | Abstract: | We consider the contour representation of the infinite volume Ising model at low temperature. Fix a subset V of Z^d, and a (large) N such that calling G_{N,V} the set of contours of length at least N intersecting V, there are in average one contour in G_{N,V} under the infinite volume "plus" measure. We find bounds on the total variation distance between the law of the contours of lenght at least N intersecting V under the "plus" measure and a Poisson process. The proof builds on the Chen-Stein method as presented by Arratia, Goldstein and Gordon. The control of the correlations is obtained through the loss-network space-time representation of contours due to Fernandez, Ferrari and Garcia. | | Source: | arXiv, math.PR/9912136 | | Services: | Forum | Review | PDF | Favorites | |
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