2020/09/28 by Matthias Birkner, Birkner, Matthias, Iulia Dahmer +5
Mathematics · Physics and Astronomy · #60J90 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2009.13642
openalex publication_date 2020/09/28 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We consider Beta(2-α, α)-coalescents with parameter range 1 <α<2 starting from n leaves. The length ℓ(n)r of order r in the n-Beta(2-α, α)-coalescent tree is defined as the sum of the lengths of all branches that carry a subtree with r leaves. We show that for any s ∈ \mathbb N the vector of suitably centered and rescaled lengths of orders 1≤ r ≤ s converges in distribution to a multivariate stable distribution as the number of leaves tends to infinity.