Yule processes with rare mutation and their applications to percolation\n on b-ary trees

2014/09/10 by Gabriel Berzunza, Berzunza, Gabriel
Mathematics · Physics and Astronomy · #60F05 #60J80 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1409.3051

openalex publication_date 2014/09/10 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

We consider supercritical Bernoulli bond percolation on a large b-ary tree,\nin the sense that with high probability, there exists a giant cluster. We show\nthat the size of the giant cluster has non-gaussian fluctuations, which extends\na result due to Schweinsberg in the case of random recursive trees. Using ideas\nin the recent work of Bertoin and Uribe Bravo, the approach developed in this\nwork relies on the analysis of the sub-population with ancestral type in a\nsystem of branching processes with rare mutations, which may be of independent\ninterest. This also allows us to establish the analogous result for scale-free\ntrees.\n

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