A Polya-like urn arises in studying stationary distributions and stationary sampling distributions in neutral (Fleming-Viot) genetics models with bounded mutation rates. This paper gives a detailed analysis of asymptotic properties of the urn. In particular, it is shown that in a sample of size...

The exclusion process is an interacting particle system in which particles perform random walks on a lattice except that they may not move to a position already occupied. In this paper we show how techniques derived from quantum mechanics may be used to achieve asymptotic results for an...

Ranked and size-biased permutations are particular functions on the set of probability measures on the simplex. They represent two recently studied schemes for relabelling groups in certain stochastic models, and are of particular interest in describing the limiting behaviour of such models. We...

This paper is concerned with the approximation of early stages of epidemic processes by branching processes. A general model for an epidemic in a closed, homogeneously mixing population is presented. A construction of a sequence of such epidemics, indexed by the initial number of susceptibles N,...