Stepping-Stone Model with Circular Brownian Migration
Printed: Mar 2008
In this paper we consider the stepping-stone model on a circle with
circular Brownian migration. We first point out a connection between
Arratia flow on the circle and the marginal distribution of this
model. We then give a new representation for the stepping-stone
model using Arratia flow and circular coalescing Brownian motion.
Such a representation enables us to carry out some explicit
computations. In particular, we find the distribution for the first
time when there is only one type
left across the circle.
stepping-stone model, circular coalescing Brownian motion, Arratia flow, duality, entrance law
60G57 - Random measures
60J65 - Brownian motion [See also 58J65]