## Electronic Communications in Probability

### Asymptotic number of caterpillars of regularly varying $\Lambda$-coalescents that come down from infinity

Batı Şengül

#### Abstract

In this paper we look at the asymptotic number of $r$-caterpillars for $\Lambda$-coalescents which come down from infinity, under a regularly varying assumption. An $r$-caterpillar is a functional of the coalescent process started from $n$ individuals which, roughly speaking, is a block of the coalescent at some time, formed by one line of descend to which $r-1$ singletons have merged one by one. We show that the number of $r$-caterpillars, suitably scaled, converge to an explicit constant as the sample size $n$ goes to $\infty$.

#### Article information

Source
Electron. Commun. Probab., Volume 22 (2017), paper no. 48, 12 pp.

Dates
Accepted: 28 August 2017
First available in Project Euclid: 2 October 2017

https://projecteuclid.org/euclid.ecp/1506931448

Digital Object Identifier
doi:10.1214/17-ECP81

Mathematical Reviews number (MathSciNet)
MR3710804

Zentralblatt MATH identifier
06797801

#### Citation

Şengül, Batı. Asymptotic number of caterpillars of regularly varying $\Lambda$-coalescents that come down from infinity. Electron. Commun. Probab. 22 (2017), paper no. 48, 12 pp. doi:10.1214/17-ECP81. https://projecteuclid.org/euclid.ecp/1506931448

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