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 Electronic Journal of Probability > Vol. 5 (2000) > Paper 7 open journal systems 


Two Coalescents Derived from the Ranges of Stable Subordinators

Jean Bertoin, Université Paris VI
Jim Pitman, University of California, Berkeley


Abstract
Let $M_alpha$ be the closure of the range of a stable subordinator of index $alphain ]0,1[$. There are two natural constructions of the $M_{alpha}$'s simultaneously for all $alphain ]0,1[$, 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.


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Pages: 1-17

Published on: November 10, 1999
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Electronic Journal of Probability. ISSN: 1083-6489