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2014 On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees
Jean Bertoin
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Electron. J. Probab. 19(none): 1-15 (2014). DOI: 10.1214/EJP.v19-2822

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 />

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Jean Bertoin. "On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees." Electron. J. Probab. 19 1 - 15, 2014. https://doi.org/10.1214/EJP.v19-2822

Information

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

zbMATH: 1292.60095
MathSciNet: MR3174836
Digital Object Identifier: 10.1214/EJP.v19-2822

Subjects:
Primary: 60F05
Secondary: 05C05

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Vol.19 • 2014
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