Abstract:We study the growth and isoperimetry of infinite clusters in slightly supercritical Bernoulli bond percolation on transitive nonamenable graphs under the L 2 boundedness condition (p c < p 2→2 ). Surprisingly, we find that the volume growth of infinite clusters is always purely exponential (that is, the subexponential corrections to growth are bounded) in the regime p c < p < p 2→2 , even when the ambient graph has unbounded corrections to exponential growth. For p slightly larger than p c , we establish the p… Show more
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