Emergence of Condensation in Kingman’s Model of Selection and Mutation
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- Dereich, S. & Mörters, P. Acta Appl Math (2013) 127: 17. doi:10.1007/s10440-012-9790-3
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We describe the onset of condensation in the simple model for the balance between selection and mutation given by Kingman in terms of a scaling limit theorem. Loosely speaking, this shows that the wave moving towards genes of maximal fitness has the shape of a gamma distribution. We conjecture that this wave shape is a universal phenomenon that can also be found in a variety of more complex models, well beyond the genetics context, and provide some further evidence for this.