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Almost giant clusters for percolation on large trees with logarithmic heights

This text is based on a lecture for the Sheffield Probability Day; its main purpose is to survey some recent asymptotic results about Bernoulli bond percolation on certain large random trees with logarithmic height. We also provide a general criterion for the existence of giant percolation clusters in large trees, which answers a question raised by David Croydon.

preprint2013arXivOpen access
Jean Bertoin
math.PR
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Jean Bertoin

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