Coherent random walks arising in some genetical models

Abstract
Certain stochastic models used in population genetics have the form of Markov processes in which a group of N points moves randomly on a line, and in which an equilibrium distribution exists for the relative configura­tion of the group. The properties of this equilibrium are studied, with particular reference to a certain limiting situation as N becomes large. In this limit the group of points is distributed like a large sample from a distribution which is itself subject to random variation.