Fabian Freund

activity

20082020

most citedOn the size of the block of 1 for

Ξ

-coalescents with dust

5 citations · 5 across the 4 of their papers we have counts for

collaborators

6 papers

math.PR2020

Multiple-merger genealogies -- models, consequences, inference

Fabian Freund

Trees corresponding to $Λ$ - and $Ξ$ - $n$ -coalescents can be both quite similar and fundamentally different compared to bifurcating tree models based on Kingman's $n$ -coalescent. Thi…

math.PR2019

The minimal observable clade size of exchangeable coalescents

Fabian Freund, Arno Siri-Jégousse

For $Λ$ - $n$ -coalescents with mutation, we analyse the size $O_{n}$ of the partition block of $i \in {1, \dots, n}$ at the time where the first mutation appears on the tree that affect…

math.PR2017★ 5 cited

On the size of the block of 1 for $Ξ$ -coalescents with dust

Fabian Freund, Martin Möhle

We study the frequency process $f_{1}$ of the block of 1 for a $Ξ$ -coalescent $Π$ with dust. If $Π$ stays infinite, $f_{1}$ is a jump-hold process which can be expressed…

math.PR2013

Minimal clade size in the Bolthausen-Sznitman coalescent

Fabian Freund, Arno Siri-Jégousse

This article shows the asymptotics of distribution and moments of the size $X_{n}$ of the minimal clade of a randomly chosen individual in a Bolthausen-Sznitman $n$ -coalescent for $n…

math.PR2012

On the length of an external branch in the Beta-coalescent

Jean-Stephane Dhersin, Fabian Freund, Arno Siri-Jegousse +1

In this paper, we consider Beta $(2 - α, α)$ (with $1 < α < 2$ ) and related $Λ$ -coalescents. If $T^{(n)}$ denotes the length of an external branch of the $n$ -coalescent, we prove the conve…

math.PR2008

On the number of allelic types for samples taken from exchangeable coalescents with mutation