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Supercritical percolation on large scale-free random trees


Bertoin, Jean; Uribe Bravo, Gerónimo (2015). Supercritical percolation on large scale-free random trees. Annals of Applied Probability, 25(1):81-103.

Abstract

We consider Bernoulli bond percolation on a large scale-free tree in the supercritical regime, meaning informally that there exists a giant cluster with high probability. We obtain a weak limit theorem for the sizes of the next largest clusters, extending a recent result in Bertoin [Random Structures Algorithms 44 (2014) 29-44] for large random recursive trees. The approach relies on the analysis of the asymptotic behavior of branching processes subject to rare neutral mutations, which may be of independent interest.

Abstract

We consider Bernoulli bond percolation on a large scale-free tree in the supercritical regime, meaning informally that there exists a giant cluster with high probability. We obtain a weak limit theorem for the sizes of the next largest clusters, extending a recent result in Bertoin [Random Structures Algorithms 44 (2014) 29-44] for large random recursive trees. The approach relies on the analysis of the asymptotic behavior of branching processes subject to rare neutral mutations, which may be of independent interest.

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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:February 2015
Deposited On:27 Jan 2016 10:06
Last Modified:05 Apr 2016 19:16
Publisher:Institute of Mathematical Statistics
ISSN:1050-5164
Publisher DOI:https://doi.org/10.1214/13-AAP988

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