Poisson approximation for large-contours in low-temperature Ising models
概率论
2011-11-10 v1 数学物理
math.MP
摘要
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.
引用
@article{arxiv.math/9912136,
title = {Poisson approximation for large-contours in low-temperature Ising models},
author = {Pablo A. Ferrari and Pierre Picco},
journal= {arXiv preprint arXiv:math/9912136},
year = {2011}
}
备注
10 pages, to appear in Physica A