Yule processes with rare mutation and their applications to percolation on b-ary trees

Berzunza, Gabriel (2014) Yule processes with rare mutation and their applications to percolation on b-ary trees Electronic Journal of Probability, 20 (none). ISSN 1083-6489

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Abstract

We consider supercritical Bernoulli bond percolation on a large $b$-ary tree, in the sense that with high probability, there exists a giant cluster. We show that the size of the giant cluster has non-gaussian fluctuations, which extends a result due to Schweinsberg in the case of random recursive trees. Using ideas in the recent work of Bertoin and Uribe Bravo, the approach developed in this work relies on the analysis of the sub-population with ancestral type in a system of branching processes with rare mutations, which may be of independent interest. This also allows us to establish the analogous result for scale-free trees.

Item Type:	Article
Additional Information:	31 pages. arXiv admin note: text overlap with arXiv:1212.2333 by other authors
Uncontrolled Keywords:	math.PR, math.PR
Divisions:	Faculty of Science & Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	08 Jul 2021 07:50
Last Modified:	22 Apr 2026 04:22
DOI:	10.1214/ejp.v20-3789
Open Access URL:	https://doi.org/10.1214/EJP.v20-3789
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3129195
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