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A Necessary and Sufficient Condition for the Lambda-Coalescent to Come Down from Infinity.


 
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1. Title Title of document A Necessary and Sufficient Condition for the Lambda-Coalescent to Come Down from Infinity.
 
2. Creator Author's name, affiliation, country Jason Schweinsberg; University of California, Berkeley
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) coalescent, Kochen-Stone Lemma
 
3. Subject Subject classification 60J75, 60G09.
 
4. Description Abstract 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.
 
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7. Date (YYYY-MM-DD) 1999-11-23
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1013
 
10. Identifier Digital Object Identifier 10.1214/ECP.v5-1013
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 5
 
12. Language English=en
 
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