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The Λ-coalescent speed of coming down from infinity

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 υ: (0, ∞) → (0, ∞) such that Nt/υ(t) → 1, almost surely, and in Lp for any p ≥ 1, as t → 0. Our approach relies on a novel martingale technique. © Institute of Mathematical Statistics, 2010.

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Publisher copy:
10.1214/09-AOP475

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Institution:
University of Oxford
Department:
Oxford, MPLS, Statistics
Role:
Author
Journal:
Annals of Probability
Volume:
38
Issue:
1
Pages:
207-233
Publication date:
2010-01-05
DOI:
ISSN:
0091-1798
URN:
uuid:c1e3560e-6401-4cd8-b9f6-c4c4e15e6761
Source identifiers:
487692
Local pid:
pubs:487692

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