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