Percolation Clusters in Hyperbolic Tessellations


It is known that, for site percolation on the Cayley graph of a cocompact Fuchsian group of genus ≥ 2, infinitely many infinite connected clusters exist almost surely for certain values of the parameter p = P{site is open}. In such cases, the set Λ of limit points at ∞ of an infinite cluster is a perfect, nowhere dense set of Lebesgue measure 0. In this… (More)


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@inproceedings{Lalley2001PercolationCI, title={Percolation Clusters in Hyperbolic Tessellations}, author={Steven P. Lalley}, year={2001} }