The Annals of Probability

Cluster formation in a stepping-stone model with continuous, hierarchically structured sites

Steven N. Evans and Klaus Fleischmann

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A stepping-stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing "stable" Lévy processes. This model can be understood as a continuum limit of discrete state-space, two-allele, genetics models with hierarchically structured resampling and migration. The existence of a process rescaling limit on suitably related large space and time scales is established and interpreted in terms of the dynamics of cluster formation. This paper was inspired by recent work of Klenke.

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Ann. Probab., Volume 24, Number 4 (1996), 1926-1952.

First available in Project Euclid: 6 January 2003

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J60: Diffusion processes [See also 58J65] 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization 60J30

Interacting diffusion stochastic partial differential equation measure-valued process stepping-stone model Fisher-Wright diffusion cluster formation clustering coalescing Lévy process hierarchical structure resampling migration


Evans, Steven N.; Fleischmann, Klaus. Cluster formation in a stepping-stone model with continuous, hierarchically structured sites. Ann. Probab. 24 (1996), no. 4, 1926--1952. doi:10.1214/aop/1041903211.

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