| Abstract: |
| The Moran process is the canonical death-birth probability model in population genetics and impacts the development of Markov processes for decades. The model allows for celebrated diffusion limits as the Wright-Fisher diffusions or Fleming-Viot processes with rich mathematical structures, and so do its spatial generalizations, usually known as the voter models, in the context of integer lattices, which lead to super-Brownian motions.
In this talk, I will discuss mean-field diffusions in certain asymmetric generalizations of the voter models on general large finite sets. These models are considered in a pathbreaking work of Ohtsuki et al. (2006) in evolutionary game theory. There, a physics method was successfully applied to obtain the diffusion limits as one-dimensional Wright-Fisher diffusions with fully explicit coefficients. I will report on recent mathematical results for the corresponding prediction by Ohtsuki et al. This talk is in part based on joint work with J. Theodore Cox (Syracuse). |
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