We settle a problem raised by Seneta and Tavaré concerning the normalized limits of several plasm... more We settle a problem raised by Seneta and Tavaré concerning the normalized limits of several plasmid reproduction models. We also show that for countably infinitely many type branching processes the extinction probability and the mass at the origin of the supercritical limit need not be the same, in contrast to the finite type case.
... 8, No. 4, 975-994 LARGE DEVIATION PRINCIPLES FOR SOME RANDOM COMBINATORIAL STRUCTURES IN POPU... more ... 8, No. 4, 975-994 LARGE DEVIATION PRINCIPLES FOR SOME RANDOM COMBINATORIAL STRUCTURES IN POPULATION GENETICS AND BROWNIAN MOTION' BY SHUI FENG ANDFRED M. HOPPE ... LEMMA 3. 1. (3.1) lim 1-log E[exp(AKa, 0)] = A(A). ...
The behaviour of a Pólya-like urn which generates Ewens' sampling formula in population genetics ... more The behaviour of a Pólya-like urn which generates Ewens' sampling formula in population genetics is investigated. Connections are made with work of Watterson and Kingman and to the Poisson-Dirichlet distribution. The order in which novel types occur in the urn is shown to parallel the age distribution of the infinitely many alleles diffusion model and consequences of this property are explored. Finally the urn process is related to Kingman's coalescent with mutation to provide a rigorous basis for this parallel.
We settle a problem raised by Seneta and Tavaré concerning the normalized limits of several plasm... more We settle a problem raised by Seneta and Tavaré concerning the normalized limits of several plasmid reproduction models. We also show that for countably infinitely many type branching processes the extinction probability and the mass at the origin of the supercritical limit need not be the same, in contrast to the finite type case.
... 8, No. 4, 975-994 LARGE DEVIATION PRINCIPLES FOR SOME RANDOM COMBINATORIAL STRUCTURES IN POPU... more ... 8, No. 4, 975-994 LARGE DEVIATION PRINCIPLES FOR SOME RANDOM COMBINATORIAL STRUCTURES IN POPULATION GENETICS AND BROWNIAN MOTION' BY SHUI FENG ANDFRED M. HOPPE ... LEMMA 3. 1. (3.1) lim 1-log E[exp(AKa, 0)] = A(A). ...
The behaviour of a Pólya-like urn which generates Ewens' sampling formula in population genetics ... more The behaviour of a Pólya-like urn which generates Ewens' sampling formula in population genetics is investigated. Connections are made with work of Watterson and Kingman and to the Poisson-Dirichlet distribution. The order in which novel types occur in the urn is shown to parallel the age distribution of the infinitely many alleles diffusion model and consequences of this property are explored. Finally the urn process is related to Kingman's coalescent with mutation to provide a rigorous basis for this parallel.
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Papers by Fred Hoppe