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Pré-Publication, Document De Travail Année : 2013

Almost giant clusters for percolation on large trees with logarithmic heights

Jean Bertoin
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Résumé

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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Dates et versions

hal-00752249 , version 1 (15-11-2012)
hal-00752249 , version 2 (28-01-2013)

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Jean Bertoin. Almost giant clusters for percolation on large trees with logarithmic heights. 2013. ⟨hal-00752249v2⟩
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