Statistics Papers

Document Type

Journal Article

Date of this Version

2-2012

Publication Source

Probability Theory and Related Fields

Volume

152

Issue

1

Start Page

31

Last Page

51

DOI

10.1007/s00440-010-0315-6

Abstract

We consider the Ising model with inverse temperature β and without external field on sequences of graphs G n which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weakly converges to the symmetric mixture of the Ising model with + boundary conditions and the − boundary conditions on the k-regular tree with inverse temperature β. In the case where the graphs G n are expanders we derive a more detailed understanding by showing convergence of the Ising measure conditional on positive magnetization (sum of spins) to the + measure on the tree.

Copyright/Permission Statement

The final publication is available at Springer via http://dx.doi.org/[10.1007/s00440-010-0315-6.

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Date Posted: 27 November 2017

This document has been peer reviewed.