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

2013/05/21 by Jean Bertoin, Bertoin, Jean
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.48550/arxiv.1305.4762

arxiv created 2013/05/21 · openalex publication_date 2013/05/21 · arxiv updated 2013/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a Bernoulli bond percolation on a random recursive tree of size n≫ 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∼ \e^-c, and it follows from a recent result of Schweinsberg \citeSch 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.

Citations

• Supercritical percolation on large scale-free random trees

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