Electronic Communications in Probability

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

Batı Şengül

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1506931448

Digital Object Identifier
doi:10.1214/17-ECP81

Mathematical Reviews number (MathSciNet)
MR3710804

Zentralblatt MATH identifier
06797801

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J99: None of the above, but in this section 60F99: None of the above, but in this section

Keywords
coalescent processes regularly varying coalescents cherries caterpillars scaling limits

Rights
Creative Commons Attribution 4.0 International License.

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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