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.

Keywords:

stepping-stone model, circular coalescing Brownian motion, Arratia flow, duality, entrance law stepping-stone model, circular coalescing Brownian motion, Arratia flow, duality, entrance law

MSC Classifications:

60G57, 60J65 show english descriptions Random measures
Brownian motion [See also 58J65] 60G57 - Random measures
60J65 - Brownian motion [See also 58J65]

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