A probabilistic analysis of a discrete-time evolution in recombination

Abstract

We study the discrete-time evolution of a recombination transformation in population genetics. The transformation acts on a product probability space, and its evolution can be described by a Markov chain on a set of partitions that converges to the finest partition. We describe the geometric decay rate to this limit and the quasi-stationary behavior of the Markov chain when conditioned on the event that the chain does not hit the limit.