Supercritical percolation on large scale-free random trees

2012/12/11 by Jean Bertoin, Gerónimo Uribe Bravo, Geronimo Uribe Bravo · 2 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.1214/13-aap988

published as The Annals of Applied Probability, 2015, Vol. 25, No. 1, 81-103

arxiv created 2012/12/11 · openalex publication_date 2014/12/16 · arxiv updated 2016/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Citations

• Emergence of scaling in random networks

Cited by

• On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees
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