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math.PR2005
Refinements of stochastic domination
Erik I. Broman, Olle Haggstrom, Jeffrey E. Steif
In a recent paper by two of the authors, the concepts of upwards and downwards -movability were introduced, mainly as a technical tool for studying dynamical percolation of inte…
math.PR2001
Coupling and Bernoullicity in random-cluster and Potts models
Olle Haggstrom, Johan Jonasson, Russell Lyons
An explicit coupling construction of random-cluster measures is presented. As one of the applications of the construction, the Potts model on amenable Cayley graphs is shown to exh…
math.PR2000
Explicit isoperimetric constants and phase transitions in the random-cluster model
Olle Haggstrom, Johan Jonasson, Russell Lyons
The random-cluster model is a dependent percolation model that has applications in the study of Ising and Potts models. In this paper, several new results are obtained for the rand…