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arXiv · 0811.1208

Reconstruction of symmetric Potts Models

Allan Sly
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Abstract

The reconstruction problem on the tree has been studied in numerous contexts including statistical physics, information theory and computational biology. However, rigorous reconstruction thresholds have only been established in a small number of models. We prove the first exact reconstruction threshold in a non-binary model establishing the Kesten-Stigum bound for the 3-state Potts model on regular trees of large degree. We further establish that the Kesten-Stigum bound is not tight for the $q$-state Potts model when $q \geq 5$. Moreover, we determine asymptotics for the reconstruction thresholds.

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Allan Sly. 2008-11-07. Reconstruction of symmetric Potts Models. https://arxiv.org/abs/0811.1208

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