Journal of Applied Probability

Almost giant clusters for percolation on large trees with logarithmic heights

Jean Bertoin

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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.

Article information

Source
J. Appl. Probab., Volume 50, Number 3 (2013), 603-611.

Dates
First available in Project Euclid: 5 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1378401225

Digital Object Identifier
doi:10.1239/jap/1378401225

Mathematical Reviews number (MathSciNet)
MR3102504

Zentralblatt MATH identifier
1283.60119

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 05C05: Trees

Keywords
Random tree percolation giant component

Citation

Bertoin, Jean. Almost giant clusters for percolation on large trees with logarithmic heights. J. Appl. Probab. 50 (2013), no. 3, 603--611. doi:10.1239/jap/1378401225. https://projecteuclid.org/euclid.jap/1378401225


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