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Stepping-Stone Model with Circular Brownian Migration

Published online by Cambridge University Press:  20 November 2018

Xiaowen Zhou
Xiaowen Zhou*
Affiliation:
Department of Mathematica and Statistics, Concordia University, Montreal, QC, H3G 1M8 e-mail: xzhou@mathstat.concordia.ca
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Abstract

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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

60G5760J65stepping-stonemodelcircular coalescing Brownian motionArratia flowdualityentrance Law
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 1 , 01 March 2008 , pp. 146 - 160
Copyright
Copyright © Canadian Mathematical Society 2008

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