The Λ-coalescent speed of coming down from infinity

The Λ-coalescent speed of coming down from infinity

Julien Berestycki, Nathanaël Berestycki, and Vlada Limic

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

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 N_t of blocks at any positive time t>0). We exhibit a deterministic function v:(0, ∞)→(0, ∞) such that N_t/v(t)→1, almost surely, and in L^p for any p≥1, as t→0. Our approach relies on a novel martingale technique.

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Primary Subjects: 60J25, 60F99, 92D25

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

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1264433997
Digital Object Identifier: doi:10.1214/09-AOP475
Zentralblatt MATH identifier: 05678678
Mathematical Reviews number (MathSciNet): MR2599198

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