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Stepping-Stone Model with Circular Brownian Migration

  Published:2008-03-01
 Printed: Mar 2008
  • Xiaowen Zhou
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Abstract

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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