Uniqueness thresholds on trees versus graphs

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1897-1909
Number of pages13
JournalAnnals of Applied Probability
Issue number5
StatePublished - Oct 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Potts model
  • Uniqueness


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