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2017 Asymptotic number of caterpillars of regularly varying $\Lambda $-coalescents that come down from infinity
Batı Şengül
Electron. Commun. Probab. 22: 1-12 (2017). DOI: 10.1214/17-ECP81

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 $.

Citation

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Batı Şengül. "Asymptotic number of caterpillars of regularly varying $\Lambda $-coalescents that come down from infinity." Electron. Commun. Probab. 22 1 - 12, 2017. https://doi.org/10.1214/17-ECP81

Information

Received: 7 December 2016; Accepted: 28 August 2017; Published: 2017
First available in Project Euclid: 2 October 2017

zbMATH: 06797801
MathSciNet: MR3710804
Digital Object Identifier: 10.1214/17-ECP81

Subjects:
Primary: 60F99, 60J80, 60J99

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