A probabilistic analysis of a continuous-time evolution in recombination

Abstract

We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on a set of partitions that converges to the finest partition. We study an explicit form of the law of this process by using a family of trees. We also describe the geometric decay rate to the finest partition and the quasi-stationary behavior of the Markov chain when conditioned on the event that the chain does not hit the limit.