The Annals of Applied Probability

Supercritical percolation on large scale-free random trees

Jean Bertoin and Gerónimo Uribe Bravo

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

First available in Project Euclid: 16 December 2014

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Zentralblatt MATH identifier

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

Random tree preferential attachment percolation


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.

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