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Abstract We give a sufficient criterion for the weak disorder regime of directed polymers in random environment, which extends a well-known second moment criterion. We use a stochastic representationâ€¦ (More)

Let Î› be a finite measure on the unit interval. A Î›-Fleming-Viot process is a probability measure valued Markov process which is dual to a coalescent with multiple collisions (Î›-coalescent) inâ€¦ (More)

- Matthias C. F. Birkner, Jochen Blath, Bjarki Eldon
- Genetics
- 2013

A large offspring-number diploid biparental multilocus population model of Moran type is our object of study. At each time step, a pair of diploid individuals drawn uniformly at random contributesâ€¦ (More)

- Matthias C. F. Birkner, Jochen Blath, Matthias SteinrÃ¼cken
- Theoretical population biology
- 2011

We present and discuss new importance sampling schemes for the approximate computation of the sample probability of observed genetic types in the infinitely many sites model from population genetics.â€¦ (More)

- Bjarki Eldon, Matthias C. F. Birkner, Jochen Blath, Fabian Freund
- Genetics
- 2015

The ability of the site-frequency spectrum (SFS) to reflect the particularities of gene genealogies exhibiting multiple mergers of ancestral lines as opposed to those obtained in the presence ofâ€¦ (More)

- Matthias C. F. Birkner, Jochen Blath
- Journal of mathematical biology
- 2008

One of the central problems in mathematical genetics is the inference of evolutionary parameters of a population (such as the mutation rate) based on the observed genetic types in a finite DNAâ€¦ (More)

- Matthias C. F. Birkner, JOS E ALFREDO L OPEZ-MIMBELA
- 2002

Statistical properties of the site-frequency spectrum associated with L-coalescents are our objects of study. In particular, we derive recursions for the expected value, variance, and covariance ofâ€¦ (More)

- Matthias SteinrÃ¼cken, Matthias C. F. Birkner, Jochen Blath
- Theoretical population biology
- 2013

We apply recently developed inference methods based on general coalescent processes to DNA sequence data obtained from various marine species. Several of these species are believed to exhibitâ€¦ (More)

- Matthias C. F. Birkner, JosÃ© Alfredo LÃ³pez-Mimbela, Anton Wakolbinger

We study a semilinear PDE generalizing the Fujita equation whose evolution operator is the sum of a fractional power of the Laplacian and a convex non-linearity. Using the Feynman-Kac representationâ€¦ (More)