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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 6 January 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1041903211

Digital Object Identifier
doi:10.1214/aop/1041903211

Mathematical Reviews number (MathSciNet)
MR1415234

Zentralblatt MATH identifier
0871.60090

Subjects
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

Keywords
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

Citation

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. https://projecteuclid.org/euclid.aop/1041903211


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