Abstract. Let Xn 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 Xn. The basic observation for its proof is thatâ€¦ (More)

Abstract We study the total branch length Ln of the Bolthausen-Sznitman coalescent as the sample size n tends to infinity. Asymptotic expansions for the moments of Ln are presented. It is shown thatâ€¦ (More)

Expansions are provided for the moments of the number of collisions Xn in the Î²(2, b)-coalescent restricted to the set {1, . . . , n}. We verify that Xn/EXn converges almost surely to one and thatâ€¦ (More)

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching andâ€¦ (More)

We study the total branch length Ln of the Bolthausenâ€“Sznitman coalescent as the sample size n tends to infinity. Asymptotic expansions for the moments of Ln are presented. It is shown that Ln/E(Ln)â€¦ (More)

Let X1, X2, . . . be a sequence of random variables satisfying the distributional recursion X1 = 0 and Xn d = Xnâˆ’In + 1 for n = 2, 3, . . ., where In is a random variable with values in {1, . . . , nâ€¦ (More)