## Electronic Journal of Probability

### Clustering Behavior of a Continuous-Sites Stepping-Stone Model with Brownian Migration

Xiaowen Zhou

#### Abstract

Clustering behavior is studied for a continuous-sites stepping-stone model with Brownian migration. It is shown that, if the model starts with the same mixture of different types of individuals over each site, then it will evolve in a way such that the site space is divided into disjoint intervals where only one type of individuals appear in each interval. Those intervals (clusters) are growing as time $t$ goes to infinity. The average size of the clusters at a fixed time $t$ is of the order of square root of $t$. Clusters at different times or sites are asymptotically independent as the difference of either the times or the sites goes to infinity.

#### Article information

Source
Electron. J. Probab., Volume 8 (2003), paper no. 11, 15 p.

Dates
First available in Project Euclid: 23 May 2016

https://projecteuclid.org/euclid.ejp/1464037584

Digital Object Identifier
doi:10.1214/EJP.v8-141

Mathematical Reviews number (MathSciNet)
MR1986843

Zentralblatt MATH identifier
1064.60074

#### Citation

Zhou, Xiaowen. Clustering Behavior of a Continuous-Sites Stepping-Stone Model with Brownian Migration. Electron. J. Probab. 8 (2003), paper no. 11, 15 p. doi:10.1214/EJP.v8-141. https://projecteuclid.org/euclid.ejp/1464037584

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