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Let X n be the number of cuts needed to isolate the root in a random recursive tree with n vertices. We provide a weak convergence result for X n. The basic observation for its proof is that the probability distributions of). This distributional recursion was not studied previously in the sense of weak convergence.
A spectral decomposition for the generator and the transition probabilities of the block counting process of the Bolthausen–Sznitman coalescent is derived. This decomposition is closely related to the Stirling numbers of the first and second kind. The proof is based on generating functions and exploits a certain factorization property of the(More)
We study the total branch length L n of the Bolthausen-Sznitman co-alescent as the sample size n tends to infinity. Asymptotic expansions for the moments of Ln are presented. It is shown that Ln/E(Ln) converges to 1 in probability and that L n , properly normalized, converges weakly to a stable random variable as n tends to infinity. The results are applied(More)
Let X 1 , X 2 ,. .. be a sequence of random variables satisfying the distributional recursion X 1 = 0 and X n d can be interpreted as the absorption time of a suitable death Markov chain with state space N := {1, 2,. . .} and absorbing state 1, conditioned that the chain starts in the initial state n. This paper focuses on the asymptotics of X n as n tends(More)
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