Positive association in the fractional fuzzy Potts model

Jeff Kahn, Nicholas Weininger

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


A fractional fuzzy Potts measure is a probability distribution on spin configurations of a finite graph G obtained in two steps: first a subgraph of G is chosen according to a random cluster measure Φp,q, and then a spin (±1) is chosen independently for each component of the subgraph and assigned to all vertices of that component. We show that whenever q ≥1, such a measure is positively associated, meaning that any two increasing events are positively correlated. This generalizes earlier results of Häggström [Ann. Appl. Probab. 9 (1999) 1149-1159] and Häggström and Schramm [Stochastic Process. Appl. 96 (2001) 213-242].

Original languageEnglish (US)
Pages (from-to)2038-2043
Number of pages6
JournalAnnals of Probability
Issue number6
StatePublished - 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Cluster model
  • Fuzzy potts model
  • Positive association
  • Random


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