Reconstruction of symmetric Potts Models

Details Reconstruction of symmetric Potts Models Reconstruction of symmetric Potts Models

2008-11-07

arxiv.org/abs/0811.1208v1

Mathematics

Probability

Scientific paper

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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