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Berestycki, Julien; Berestycki, Nathanaël; Limic, Vlada

The \(\Lambda \)-coalescent speed of coming down from infinity. (English) Zbl 1247.60110

Ann. Probab. 38, No. 1, 207-233 (2010).
Authors’ abstract: Consider a \(\Lambda \)-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 \(v:(0, \infty)\rightarrow (0, \infty )\) such that \(N_t/v(t)\rightarrow 1\), almost surely, and in \(L^p\) for any \(p\geq 1\), as \(t\rightarrow 0\). Our approach relies on a novel martingale technique.
Reviewer: Valentin Topchii (Omsk)

Cited in 2 Reviews
Cited in 25 Documents

MSC:

60J25 Continuous-time Markov processes on general state spaces
60F99 Limit theorems in probability theory
92D25 Population dynamics (general)

Keywords:

exchangeable coalescents; small-time asymptotics; coming down from infinity; martingale techniques; fluid limits
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\textit{J. Berestycki} et al., Ann. Probab. 38, No. 1, 207--233 (2010; Zbl 1247.60110)
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