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Poisson approximation for large-contours in low-temperature Ising models - MaRDI portal

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Poisson approximation for large-contours in low-temperature Ising models

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Publication:6502862

DOI10.1016/S0378-4371(99)00536-1arXivmath/9912136MaRDI QIDQ6502862

Author name not available (Why is that?)


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.





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