Open Access
November 2007 Positive association in the fractional fuzzy Potts model
Jeff Kahn, Nicholas Weininger
Ann. Probab. 35(6): 2038-2043 (November 2007). DOI: 10.1214/009117907000000042


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].


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Jeff Kahn. Nicholas Weininger. "Positive association in the fractional fuzzy Potts model." Ann. Probab. 35 (6) 2038 - 2043, November 2007.


Published: November 2007
First available in Project Euclid: 8 October 2007

zbMATH: 1128.60085
MathSciNet: MR2353381
Digital Object Identifier: 10.1214/009117907000000042

Primary: 60C05
Secondary: 05D40

Keywords: fuzzy Potts model , positive association , random cluster model

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 6 • November 2007
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