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January 2010 The Λ-coalescent speed of coming down from infinity
Julien Berestycki, Nathanaël Berestycki, Vlada Limic
Ann. Probab. 38(1): 207-233 (January 2010). DOI: 10.1214/09-AOP475


Consider a Λ-coalescent that comes down from infinity (meaning that it starts from a configuration containing infinitely many blocks at time 0, yet it has a finite number Nt of blocks at any positive time t>0). We exhibit a deterministic function v:(0, ∞)→(0, ∞) such that Nt/v(t)→1, almost surely, and in Lp for any p≥1, as t→0. Our approach relies on a novel martingale technique.


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Julien Berestycki. Nathanaël Berestycki. Vlada Limic. "The Λ-coalescent speed of coming down from infinity." Ann. Probab. 38 (1) 207 - 233, January 2010.


Published: January 2010
First available in Project Euclid: 25 January 2010

zbMATH: 1247.60110
MathSciNet: MR2599198
Digital Object Identifier: 10.1214/09-AOP475

Primary: 60F99 , 60J25 , 92D25

Keywords: coming down from infinity , Exchangeable coalescents , fluid limits , martingale techniques , small-time asymptotics

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 1 • January 2010
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