Reconstruction for the Asymmetric Ising Model on Regular Trees

Wenjian Liu; Ning Ning

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arXiv · 1712.00395

Reconstruction for the Asymmetric Ising Model on Regular Trees

Wenjian Liu·Ning Ning

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Abstract

It is known that the Kesten-Stigum reconstruction bound is tight for roughly symmetric binary channels. In this paper, we will adopt a refined analysis of moment recursion on a weighted version of the magnetization, which is engaged in Sly [2011] to handle the symmetric Potts model, and establish the critical condition of the asymmetric Ising model to make Kesten-Stigum bound the reconstruction threshold on regular $d$-ary trees.

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Wenjian Liu, Ning Ning. 2017-12-01. Reconstruction for the Asymmetric Ising Model on Regular Trees. https://arxiv.org/abs/1712.00395

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