Geodesic
Stepping-Stone Model with Circular Brownian Migration
Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 146-160

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DOI

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.
DOI : 10.4153/CMB-2008-017-2
Mots-clés : 60G57, 60J65, stepping-stonemodel, circular coalescing Brownian motion, Arratia flow, duality, entrance Law 
Zhou, Xiaowen. Stepping-Stone Model with Circular Brownian Migration. Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 146-160. doi: 10.4153/CMB-2008-017-2
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     author = {Zhou, Xiaowen},
     title = {Stepping-Stone {Model} with {Circular} {Brownian} {Migration}},
     journal = {Canadian mathematical bulletin},
     pages = {146--160},
     year = {2008},
     volume = {51},
     number = {1},
     doi = {10.4153/CMB-2008-017-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-017-2/}
}
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