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

Jean Bertoin (1)

1 Institut für Mathematik [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 $G_n\sim \e^{-c}$. We show here that $G_n$ has non-gaussian fluctuations. The approach relies on the analysis of the effect of percolation on different phases of the growth of recursive trees. After posting this paper, I realized that the main result of the manuscript follows directly from an article by Jason Schweinsberg "Dynamics of the evolving Bolthausen-Sznitman coalescent" Electron. J. Probab. 17 (2012).

Mots clés: Random recursive tree; giant cluster; fluctuations; super-critical percolation.; super-critical percolation

Domaines: Probabilités [math.PR]

Jean Bertoin. Non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees. 2013. ⟨hal-00819320v1⟩