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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

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.

Citation

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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. https://doi.org/10.1214/09-AOP475

Information

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

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

Subjects:
Primary: 60F99, 60J25, 92D25

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 1 • January 2010
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