Emergence of condensation in Kingman's model of selection and mutation

Steffen Dereich; Peter Mörters

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arXiv · 1207.6203

Emergence of condensation in Kingman's model of selection and mutation

Steffen Dereich·Peter Mörters

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Abstract

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.

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Steffen Dereich, Peter Mörters. 2012-07-26. Emergence of condensation in Kingman's model of selection and mutation. https://arxiv.org/abs/1207.6203

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