Almost giant clusters for percolation on large trees with logarithmic heights

2012/11/16 by Jean Bertoin, Bertoin, Jean
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1211.3822

arxiv created 2013/01/28 · arxiv updated 2013/01/29

Abstract

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.

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