A homological upper bound on critical probabilities for hyperbolic percolation

Published 18 Aug 2014 in math.PR and math.CO | (1408.4031v2)

Abstract: We study bond percolation for a family of infinite hyperbolic graphs. We relate percolation to the appearance of homology in finite versions of these graphs. As a consequence, we derive an upper bound on the critical probabilities of the infinite graphs.

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