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October 2008 Uniqueness thresholds on trees versus graphs
Allan Sly
Ann. Appl. Probab. 18(5): 1897-1909 (October 2008). DOI: 10.1214/07-AAP508

Abstract

Counter to the general notion that the regular tree is the worst case for decay of correlation between sets and nodes, we produce an example of a multi-spin interacting system which has uniqueness on the d-regular tree but does not have uniqueness on some infinite d-regular graphs.

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Allan Sly. "Uniqueness thresholds on trees versus graphs." Ann. Appl. Probab. 18 (5) 1897 - 1909, October 2008. https://doi.org/10.1214/07-AAP508

Information

Published: October 2008
First available in Project Euclid: 30 October 2008

zbMATH: 1214.82021
MathSciNet: MR2462553
Digital Object Identifier: 10.1214/07-AAP508

Subjects:
Primary: 82B26

Keywords: Potts model, uniqueness

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.18 • No. 5 • October 2008
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