A coarse graining for the Fortuin-Kasteleyn measure in random media

Marc Wouts

Stochastic Processes and their Applications, 2008, vol. 118, issue 11, 1929-1972

Abstract: By means of a multi-scale analysis we describe the typical geometrical structure of the clusters under the FK measure in random media. Our result holds in any dimension d[greater-or-equal, slanted]2 provided that slab percolation occurs under the averaged measure, which should be the case for the whole supercritical phase. This work extends that of Pisztora [A. Pisztora, Surface order large deviations for Ising, Potts and percolation models, Probab. Theory Related Fields 104 (4) (1996) 427-466] and provides an essential tool for the analysis of the supercritical regime in disordered FK models and in the corresponding disordered Ising and Potts models.

Keywords: Coarse; graining; Multi-scale; analysis; Random; media; Fortuin-Kasteleyn; measure; Dilute; Ising; model (search for similar items in EconPapers)
Date: 2008
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