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On the Speed of Coming Down from Infinity for $\Xi$-Coalescent Processes

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	On the Speed of Coming Down from Infinity for $\Xi$-Coalescent Processes
2.	Creator	Author's name, affiliation, country	Vlada Limic; CNRS and Université de Provence; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Exchangeable coalescents; small-time asymptotics; coming down from infinity; martingale technique
3.	Subject	Subject classification	60J25; 60F99; 92D25
4.	Description	Abstract	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Institut Mittag-Leffler, ANR MAEV grant
7.	Date	(YYYY-MM-DD)	2010-03-01
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/742
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-742
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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