On the behavior of LIFO preemptive resume queues in heavy traffic.
On the speed of coming down from infinity for -coalescent processes.
The entrance boundary of the multiplicative coalescent.
The spatial -coalescent.
The Beurling estimate for a class of random walks.
Representation theorems for interacting Moran models, interacting Fisher-Wright diffusions and applications.
Genealogies of regular exchangeable coalescents with applications to sampling
This article considers a model of genealogy corresponding to a regular exchangeable coalescent (also known as -coalescent) started from a large finite configuration, and undergoing neutral mutations. Asymptotic expressions for the number of active lineages were obtained by the author in a previous work. Analogous results for the number of active mutation-free lineages and the combined lineage lengths are derived using the same martingale-based technique. They are given in terms of convergence in...
Asymptotic sampling formulae for -coalescents
We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy is given by a -coalescent. This allows us to derive an exact formula for the asymptotic behavior of the site and allele frequency spectrum and the number of segregating sites, as the sample size tends to . Some of our results hold in the case of a general -coalescent...
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