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Two Coalescents Derived from the Ranges of Stable Subordinators


 
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1. Title Title of document Two Coalescents Derived from the Ranges of Stable Subordinators
 
2. Creator Author's name, affiliation, country Jean Bertoin; Université Paris VI
 
2. Creator Author's name, affiliation, country Jim Pitman; University of California, Berkeley
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) coalescent, stable, subordinator, Poisson-Dirichlet distribution
 
3. Subject Subject classification 60J30, 60J25.
 
4. Description Abstract Let $M_\alpha$ be the closure of the range of a stable subordinator of index $\alpha\in ]0,1[$. There are two natural constructions of the $M_{\alpha}$'s simultaneously for all $\alpha\in ]0,1[$, so that $M_{\alpha}\subseteq M_{\beta}$ for $0< \alpha < \beta < 1$: one based on the intersection of independent regenerative sets and one based on Bochner's subordination. We compare the corresponding two coalescent processes defined by the lengths of complementary intervals of $[0,1]\backslash M_{1-\rho}$ for $0 < \rho < 1$. In particular, we identify the coalescent based on the subordination scheme with the coalescent recently introduced by Bolthausen and Sznitman.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 1999-11-10
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/63
 
10. Identifier Digital Object Identifier 10.1214/EJP.v5-63
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 5
 
12. Language English=en
 
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