Open Access
Translator Disclaimer
2010 On the Speed of Coming Down from Infinity for $\Xi$-Coalescent Processes
Vlada Limic
Author Affiliations +
Electron. J. Probab. 15: 217-240 (2010). DOI: 10.1214/EJP.v15-742


The $\Xi$-coalescent processes were initially studied by Möhle and Sagitov (2001), and introduced by Schweinsberg (2000) in their full generality. They arise in the mathematical population genetics as the complete class of scaling limits for genealogies of Cannings' models. The $\Xi$-coalescents generalize $\Lambda$-coalescents, where now simultaneous multiple collisions of blocks are possible. The standard version starts with infinitely many blocks at time $0$, and it is said to come down from infinity if its number of blocks becomes immediately finite, almost surely. This work builds on the technique introduced recently by Berstycki, Berestycki and Limic (2009), and exhibits deterministic ``speed'' function - an almost sure small time asymptotic to the number of blocks process, for a large class of $\Xi$-coalescents that come down from infinity.


Download Citation

Vlada Limic. "On the Speed of Coming Down from Infinity for $\Xi$-Coalescent Processes." Electron. J. Probab. 15 217 - 240, 2010.


Accepted: 1 March 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1203.60111
MathSciNet: MR2594877
Digital Object Identifier: 10.1214/EJP.v15-742

Primary: 60J25
Secondary: 60F99 , 92D25

Keywords: coming down from infinity , Exchangeable coalescents , martingale technique , small-time asymptotics


Vol.15 • 2010
Back to Top