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

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  • Wouts, Marc

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.

Suggested Citation

  • Wouts, Marc, 2008. "A coarse graining for the Fortuin-Kasteleyn measure in random media," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1929-1972, November.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:11:p:1929-1972
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