The Λ-coalescent speed of coming down from infinity
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, almo...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2010
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| Summary: | 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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