Positive association in the fractional fuzzy potts model
成果类型：
Article
署名作者：
Kahn, Jeff; Weininger, Nicholas
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117907000000042
发表日期：
2007
页码：
2038-2043
关键词：
摘要：
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 phi(p,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 Haggstrom [Ann. Appl. Probab. 9 (1999) 1149-1159] and Haggstrom and Schramm [Stochastic Process. Appl. 96 (2001) 213-242].