Fluctuation Theory for Moran’s Genetics Model

A genetics model of Moran}which includes the Bernoulli]Laplace urn as a special case}is examined to give a picture of the model’s fluctuation theory and asymptotics as the number of states grows large, with particular attention to the time of passage between extreme states. These passage times are shown to have means which grow exponentially with the number of states, and when normalised converge weakly to an exponential distribution