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).

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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, 60F05, 60J80
Divisions: Faculty of Science and Engineering > School of Physical Sciences
Depositing User: Symplectic Admin
Date Deposited: 08 Jul 2021 07:50
Last Modified: 17 Mar 2024 09:06
DOI: 10.1214/ejp.v20-3789
Open Access URL: https://doi.org/10.1214/EJP.v20-3789
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3129195