The Annals of Probability

The Λ-coalescent speed of coming down from infinity

Julien Berestycki, Nathanaël Berestycki, and Vlada Limic

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Abstract

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.

Article information

Source
Ann. Probab. Volume 38, Number 1 (2010), 207-233.

Dates
First available in Project Euclid: 25 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1264433997

Digital Object Identifier
doi:10.1214/09-AOP475

Mathematical Reviews number (MathSciNet)
MR2599198

Zentralblatt MATH identifier
1247.60110

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces 60F99: None of the above, but in this section 92D25: Population dynamics (general)

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

Citation

Berestycki, Julien; Berestycki, Nathanaël; Limic, Vlada. The Λ-coalescent speed of coming down from infinity. Ann. Probab. 38 (2010), no. 1, 207--233. doi:10.1214/09-AOP475. https://projecteuclid.org/euclid.aop/1264433997


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