Acta Applicandae Mathematicae

, Volume 127, Issue 1, pp 17–26

Emergence of Condensation in Kingman’s Model of Selection and Mutation

Article

DOI: 10.1007/s10440-012-9790-3

Cite this article as:
Dereich, S. & Mörters, P. Acta Appl Math (2013) 127: 17. doi:10.1007/s10440-012-9790-3

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.

Keywords

House of cards model Bose-Einstein condensation Condensation wave Selection Mutation Gamma distribution Universality Random permutations Random network Fitness distribution 

Mathematics Subject Classification

92D10 37N25 82B26 92D15 

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Institut für Mathematische StatistikUniversität MünsterMünsterGermany
  2. 2.Department of Mathematical SciencesUniversity of BathBathUK

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