Perturbation Theory and the Renormalization Group in Genetic Dynamics

Stephens, C. R. and Zamora, A. and Wright, A. (2004) Perturbation Theory and the Renormalization Group in Genetic Dynamics. (Preprint)

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Although much progress has been made in recent years in the theory of GAs and GP, there is still a conspicuous lack of tools with which to derive systematic, approximate solutions to their dynamics. In this article we propose and study perturbation theory as a potential tool to fill this gap. We concentrate mainly on selection-mutation systems, showing different implementations of the perturbative framework, developing, for example, perturbative expansions for the eigenvalues and eigenvectors of the transition matrix. The main focus however, is on diagrammatic methods, taken from physics, where we show how approximations can be built up using a pictorial representation generated by a simple set of rules, and how the renormalization group can be used to systematically improve the perturbation theory.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 13 Jun 2018 14:37
Last Modified: 17 Dec 2022 20:16

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