随机介质中Fortuin-Kasteleyn测度的粗粒化
A coarse graining for the Fortuin-Kasteleyn measure in random media
摘要：
通过多尺度分析，我们描述了随机介质中FK测度下团簇的典型几何结构。我们的结果适用于任何尺寸大于或等于2的条件下，平板渗流发生在平均措施，这应该是在整个超临界相的情况。这项工作扩展了Pisztora的工作，并为无序FK模型和相应的无序Ising和Potts模型中的超临界区的分析提供了一个必要的工具。
英文摘要：
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 greater or equal to 2 provided that slab percolation occurs under the averaged measure, which should be the case in the whole supercritical phase. This work extends the one of Pisztora 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.
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