The asymptotic distribution of cluster sizes for supercritical percolation on random split trees

Berzunza, Gabriel and Holmgren, Cecilia (2020) The asymptotic distribution of cluster sizes for supercritical percolation on random split trees. Random Structures & Algorithms, 60 (4). pp. 631-652.

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Official URL: http://dx.doi.org/10.1002/rsa.21046

Abstract

We consider the model of random trees introduced by Devroye (1999), the so-called random split trees. The model encompasses many important randomized algorithms and data structures. We then perform supercritical Bernoulli bond-percolation on those trees and obtain a precise weak limit theorem for the sizes of the largest clusters. We also show that the approach developed in this work may be useful for studying percolation on other classes of trees with logarithmic height, for instance, we study also the case of $d$-regular trees.

Item Type:	Article
Additional Information:	25 pages
Uncontrolled Keywords:	math.PR, math.PR, 60C05, 60F05, 60K35, 68P05, 05C05, 05C80
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	30 May 2022 14:42
Last Modified:	18 Jan 2023 21:11
DOI:	10.1002/rsa.21046
Open Access URL:	https://arxiv.org/pdf/2003.12018.pdf
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3150105