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Almost giant clusters for percolation on large trees with logarithmic heights


Bertoin, Jean (2013). Almost giant clusters for percolation on large trees with logarithmic heights. Journal of Applied Probability, 50(3):603-611.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2013
Deposited On:22 Nov 2013 11:31
Last Modified:05 Apr 2016 17:10
Publisher:Applied Probability Trust
ISSN:0021-9002
Publisher DOI:https://doi.org/10.1239/jap/1378401225

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