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Two coalescents derived from the ranges of stable subordinators


Bertoin, Jean; Pitman, Jim (2000). Two coalescents derived from the ranges of stable subordinators. Electronic Journal of Probability, 5(7):1-17.

Abstract

Let Mα be the closure of the range of a stable subordinator of index α∈]0,1[. There are two natural constructions of the Mα's simultaneously for all α∈]0,1[, so that Mα⊆Mβ for 0<α<β<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]∖M1−ρ for 0<ρ<1. In particular, we identify the coalescent based on the subordination scheme with the coalescent recently introduced by Bolthausen and Sznitman.

Abstract

Let Mα be the closure of the range of a stable subordinator of index α∈]0,1[. There are two natural constructions of the Mα's simultaneously for all α∈]0,1[, so that Mα⊆Mβ for 0<α<β<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]∖M1−ρ for 0<ρ<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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2000
Deposited On:23 Jul 2013 14:08
Last Modified:05 Apr 2016 16:52
Publisher:Institute of Mathematical Statistics
ISSN:1083-6489
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/EJP.v5-63
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1768841
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0949.60034

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