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February 2015 Supercritical percolation on large scale-free random trees
Jean Bertoin, Gerónimo Uribe Bravo
Ann. Appl. Probab. 25(1): 81-103 (February 2015). DOI: 10.1214/13-AAP988

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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Jean Bertoin. Gerónimo Uribe Bravo. "Supercritical percolation on large scale-free random trees." Ann. Appl. Probab. 25 (1) 81 - 103, February 2015. https://doi.org/10.1214/13-AAP988

Information

Published: February 2015
First available in Project Euclid: 16 December 2014

zbMATH: 1309.60094
MathSciNet: MR3297766
Digital Object Identifier: 10.1214/13-AAP988

Subjects:
Primary: 60J27, 60J80

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 1 • February 2015
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