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


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.


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

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

Primary: 60K35

Keywords: Potts model , Reconstruction problem on the tree

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 4 • July 2011
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