The Λ-coalescent speed of coming down from infinity - Berestycki, J; Berestycki, N; Limic, V (2010)
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.