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July 2011 Reconstruction for the Potts model
Allan Sly
Ann. Probab. 39(4): 1365-1406 (July 2011). DOI: 10.1214/10-AOP584

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 nonbinary 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 ≥ 5. Moreover, we determine asymptotics for these reconstruction thresholds.

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Allan Sly. "Reconstruction for the Potts model." Ann. Probab. 39 (4) 1365 - 1406, July 2011. https://doi.org/10.1214/10-AOP584

Information

Published: July 2011
First available in Project Euclid: 5 August 2011

zbMATH: 1234.60095
MathSciNet: MR2857243
Digital Object Identifier: 10.1214/10-AOP584

Subjects:
Primary: 60K35

Keywords: Potts model , Reconstruction problem on the tree

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 4 • July 2011
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