| Título: | A Necessary and Sufficient Condition for the Lambda-Coalescent to Come Down from Infinity. |
| Autores: | Schweinsberg, Jason; University of California, Berkeley |
| Fecha: | 2000-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
coalescent, Kochen-Stone Lemma 60J75, 60G09. |
| Descripción: | Let $\Pi_{\infty}$ be the standard $\Lambda$-coalescent of Pitman, which is defined so that $\Pi_{\infty}(0)$ is the partition of the positive integers into singletons, and, if $\Pi_n$ denotes the restriction of $\Pi_{\infty}$ to $\{ 1,\ldots, n \}$, then whenever $\Pi_n(t)$ has $b$ blocks, each $k$-tuple of blocks is merging to form a single block at the rate $\lambda_{b,k}$, where $\lambda_{b,k} = \int_0^1 x^{k-2} (1-x)^{b-k} \Lambda(dx)$ for some finite measure $\Lambda$. We give a necessary and sufficient condition for the $\Lambda$-coalescent to ``come down from infinity'', which means that the partition $\Pi_{\infty}(t)$ almost surely consists of only finitely many blocks for all $t > 0$. We then show how this result applies to some particular families of $\Lambda$-coalescents. |
| Idioma: | No aplica |
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