Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155663 | Stochastic Processes and their Applications | 2013 | 25 Pages |
Abstract
In this paper, we consider Beta(2âα,α) (with 1<α<2) and related Î-coalescents. If T(n) denotes the length of a randomly chosen external branch of the n-coalescent, we prove the convergence of nαâ1T(n) when n tends to â, and give the limit. To this aim, we give asymptotics for the number Ï(n) of collisions which occur in the n-coalescent until the end of the chosen external branch, and for the block counting process associated with the n-coalescent.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Jean-Stéphane Dhersin, Fabian Freund, Arno Siri-Jégousse, Linglong Yuan,