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September 2013 Almost giant clusters for percolation on large trees with logarithmic heights
Jean Bertoin
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J. Appl. Probab. 50(3): 603-611 (September 2013). DOI: 10.1239/jap/1378401225

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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Jean Bertoin. "Almost giant clusters for percolation on large trees with logarithmic heights." J. Appl. Probab. 50 (3) 603 - 611, September 2013. https://doi.org/10.1239/jap/1378401225

Information

Published: September 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1283.60119
MathSciNet: MR3102504
Digital Object Identifier: 10.1239/jap/1378401225

Subjects:
Primary: 05C05, 60K35

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 3 • September 2013
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