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Sizes of the largest clusters for supercritical percolation on random recursive trees

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Abstract

We consider Bernoulli bond-percolation on a random recursive tree of size math formula, with supercritical parameter math formula for some math formula fixed. We show that with high probability, the largest cluster has size close to math formula whereas the next largest clusters have size of order math formulaonly and are distributed according to some Poisson random measure. Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 29–44, 2014

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