Uniqueness thresholds on trees versus graphs

Details Uniqueness thresholds on trees versus graphs Uniqueness thresholds on trees versus graphs

2007-04-23

arxiv.org/abs/0704.2916v2

Annals of Applied Probability 2008, Vol. 18, No. 5, 1897-1909

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AAP508 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/07-AAP508

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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