Electronic Journal of Probability

On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees

Jean Bertoin

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We consider a Bernoulli bond percolation on a random recursive tree of size $n\gg 1$, with supercritical parameter $p_n=1-c/\ln n$ for some $c>0$ fixed. It is known that with high probability, there exists then a unique giant cluster of size $G_n\sim e^{-c}n$, and it follows from a recent result of Schweinsberg that $G_n$ has non-Gaussian fluctuations. We provide an  explanation of this  by analyzing the effect of percolation on different phases of the growth of recursive trees.  This alternative approach may be useful for studying percolation on other classes of trees, such as for instance regular trees.<br /><br />

Article information

Electron. J. Probab., Volume 19 (2014), paper no. 24, 15 pp.

Accepted: 27 February 2014
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 05C05: Trees

Random recursive tree giant cluster fluctuations super-critical percolation

This work is licensed under a Creative Commons Attribution 3.0 License.


Bertoin, Jean. On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees. Electron. J. Probab. 19 (2014), paper no. 24, 15 pp. doi:10.1214/EJP.v19-2822. https://projecteuclid.org/euclid.ejp/1465065666

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