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

Jean Bertoin (Universität Zürich)


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.

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Pages: 1-15

Publication Date: February 27, 2014

DOI: 10.1214/EJP.v19-2822


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