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Almost Giant Clusters for Percolation on Large Trees with Logarithmic Heights

Part of: Graph theory Special processes

Published online by Cambridge University Press:  30 January 2018

Jean Bertoin
Jean Bertoin*
Affiliation:
Universität Zürich
*
∗ Postal address: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland. Email address: [email protected]
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Abstract

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This paper is based on works presented at the 2012 Applied Probability Trust Lecture in Sheffield; its main purpose is to survey the recent asymptotic results of Bertoin (2012a) and Bertoin and Uribe Bravo (2012b) 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.

Keywords

Random treepercolationgiant component

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 05C05: Trees
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 3 , September 2013 , pp. 603 - 611
Copyright
© Applied Probability Trust 

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