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
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: | 07 Dec 2024 10:25 |
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 |