On asymptotics of exchangeable coalescents with multiple collisions
| dc.creator | Gnedin, Alexander | |
| dc.creator | Iksanov, Alex | |
| dc.creator | Möhle, Martin | |
| dc.date | 2008-07-17 | |
| dc.date.accessioned | 2026-07-07T09:50:59Z | |
| dc.date.available | 2026-07-07T09:50:59Z | |
| dc.description | We study the number of collisions $X_n$ of an exchangeable coalescent with multiple collisions ($Λ$-coalescent) which starts with $n$ particles and is driven by rates determined by a finite characteristic measure $ν({\rm d}x)=x^{-2}Λ({\rm d}x)$. Via a coupling technique we derive limiting laws of $X_n$, using previous results on regenerative compositions derived from stick-breaking partitions of the unit interval. The possible limiting laws of $X_n$ include normal, stable with index $1\leα<2$ and Mittag-Leffler distributions. The results apply, in particular, to the case when $ν$ is a beta$(a-2,b)$ distribution with parameters $a>2$ and $b>0$. The approach taken allows to derive asymptotics of three other functionals of the coalescent, the absorption time, the length of an external branch chosen at random from the $n$ external branches, and the number of collision events that occur before the randomly selected external branch coalesces with one of its neighbours. | |
| dc.identifier | https://arxiv.org/abs/0807.2742 | |
| dc.identifier | http://arxiv.org/abs/0807.2742 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165132 | |
| dc.subject | Probability | |
| dc.subject | 60J10, 60K15 | |
| dc.title | On asymptotics of exchangeable coalescents with multiple collisions | |
| dc.type | text |