Emergence of Condensation in Kingmans Model of Selection and Mutation
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.
selection mutation gamma distribution universality house of cards model bose-einstein condensation condensation wave random permutations random network fitness distribution 92d10 37n25 82b26 92d15