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Two Coalescents Derived from the Ranges of Stable Subordinators

   
@article{EJP63,
	author = {Jean Bertoin and Jim Pitman},
	title = {Two Coalescents Derived from the Ranges of Stable Subordinators},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {5},
	year = {1999},
	keywords = {coalescent, stable, subordinator, Poisson-Dirichlet distribution},
	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.},
	pages = {no. 7, 1-17},
	issn = {1083-6489},
	doi = {10.1214/EJP.v5-63},    
        url = {http://ejp.ejpecp.org/article/view/63}}