Uniqueness thresholds on trees versus graphs

Allan Sly

doi:10.1214/07-AAP508

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Home > Journals > Ann. Appl. Probab. > Volume 18 > Issue 5 > Article

October 2008 Uniqueness thresholds on trees versus graphs

Allan Sly

Ann. Appl. Probab. 18(5): 1897-1909 (October 2008). DOI: 10.1214/07-AAP508

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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.