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Sizes of the largest clusters for supercritical percolation on random recursive trees


Bertoin, Jean (2012). Sizes of the largest clusters for supercritical percolation on random recursive trees. Random Structures & Algorithms, 43(4):1-16.

Abstract

We consider Bernoulli bond-percolation on a random recursive tree of size n ≫ 1, with supercritical parameter p(n) = 1 - t/ln n + o(1/ln n) for some t > 0 fixed. We show that with high probability, the largest cluster has size close to e -tn whereas the next largest clusters have size of order n/ln n only and are distributed according to some Poisson random measure.

Abstract

We consider Bernoulli bond-percolation on a random recursive tree of size n ≫ 1, with supercritical parameter p(n) = 1 - t/ln n + o(1/ln n) for some t > 0 fixed. We show that with high probability, the largest cluster has size close to e -tn whereas the next largest clusters have size of order n/ln n only and are distributed according to some Poisson random measure.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:17 July 2012
Deposited On:22 Nov 2013 11:35
Last Modified:07 Dec 2017 23:54
Publisher:Wiley-Blackwell
ISSN:1042-9832
Publisher DOI:https://doi.org/10.1002/rsa.20448

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