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- Michael Drmota, Alex Iksanov, Martin Moehle, Uwe Roesler
- Random Struct. Algorithms
- 2009

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.

- Martin Möhle, Helmut Pitters
- 2014

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)

- ALEX IKSANOV, ALEX MARYNYCH, MARTIN MÖHLE
- 2009

Expansions are provided for the moments of the number of collisions Xn in the β(2, b)-coalescent restricted to the set {1,. .. , n}. We verify that Xn/EXn converges almost surely to one and that Xn, properly normalized, weakly converges to the standard normal law. These results complement previously known facts concerning the number of collisions in β(a,… (More)

- Alex Iksanov, Martin Möhle
- 2007

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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