On the Cluster Size Distribution for Percolation on Some General Graphs

• We show that for any Cayley graph, the probability (at any p) that the cluster of the origin has size n decays at a well-defined exponential rate (possibly 0). For general graphs, we relate this rate being positive in the supercritical regime with the amenability/nonamenability of the underlying graph.

Ämnesord

NATURVETENSKAP  -- Matematik -- Annan matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Other Mathematics (hsv//eng)

Nyckelord

percolation

Cayley graph

exponential decay

percolation

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