Electronic Journal of Probability

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

Jean Bertoin

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065666

Digital Object Identifier
doi:10.1214/EJP.v19-2822

Mathematical Reviews number (MathSciNet)
MR3174836

Zentralblatt MATH identifier
1292.60095

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

Keywords
Random recursive tree giant cluster fluctuations super-critical percolation

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

Citation

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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