The Annals of Applied Probability

Supercritical percolation on large scale-free random trees

Jean Bertoin and Gerónimo Uribe Bravo

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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.

Article information

Source
Ann. Appl. Probab., Volume 25, Number 1 (2015), 81-103.

Dates
First available in Project Euclid: 16 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1418740179

Digital Object Identifier
doi:10.1214/13-AAP988

Mathematical Reviews number (MathSciNet)
MR3297766

Zentralblatt MATH identifier
1309.60094

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Random tree preferential attachment percolation

Citation

Bertoin, Jean; Uribe Bravo, Gerónimo. Supercritical percolation on large scale-free random trees. Ann. Appl. Probab. 25 (2015), no. 1, 81--103. doi:10.1214/13-AAP988. https://projecteuclid.org/euclid.aoap/1418740179


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