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2000 Two Coalescents Derived from the Ranges of Stable Subordinators
Jean Bertoin, Jim Pitman
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Electron. J. Probab. 5: 1-17 (2000). DOI: 10.1214/EJP.v5-63


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 $0 \lt \alpha \lt \beta \lt 1$: 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 $0 \lt \rho \lt 1$. In particular, we identify the coalescent based on the subordination scheme with the coalescent recently introduced by Bolthausen and Sznitman.


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Jean Bertoin. Jim Pitman. "Two Coalescents Derived from the Ranges of Stable Subordinators." Electron. J. Probab. 5 1 - 17, 2000.


Accepted: 10 November 1999; Published: 2000
First available in Project Euclid: 7 March 2016

zbMATH: 0949.60034
MathSciNet: MR1768841
Digital Object Identifier: 10.1214/EJP.v5-63

Primary: 60J30
Secondary: 60J25

Keywords: Coalescent , Poisson-Dirichlet distribution , Stable , subordinator

Vol.5 • 2000
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