Stepping-Stone Model with Circular Brownian Migration

• Autores: Xiaowen Zhou
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 51, Nº 1, 2008, págs. 146-160
• Idioma: inglés
• DOI: 10.4153/cmb-2008-017-2
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• Resumen

  • 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.