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October 2000 The genealogy of a cluster in the multitype voter model
J. Theodore Cox, Jochen Geiger
Ann. Probab. 28(4): 1588-1619 (October 2000). DOI: 10.1214/aop/1019160499

Abstract

The genealogy of a cluster in the multitype voter model can be defined in terms of a family of dual coalescing random walks. We represent the genealogy of a cluster as a point process in a size-time plane and show that in high dimensions the genealogy of the cluster at the origin has a weak Poisson limit.The limiting point process is the same as for the genealogy of the size-biased Galton-Watson tree. Moreover, our results show that the branching mechanism and the spatial effects of the voter model can be separated on a macroscopic scale. Our proofs are based on a probabilistic construction of the genealogy of the cluster at the origin derived from Harris’ graphical representation of the voter model.

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J. Theodore Cox. Jochen Geiger. "The genealogy of a cluster in the multitype voter model." Ann. Probab. 28 (4) 1588 - 1619, October 2000. https://doi.org/10.1214/aop/1019160499

Information

Published: October 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1108.60317
MathSciNet: MR1813835
Digital Object Identifier: 10.1214/aop/1019160499

Subjects:
Primary: 60K35
Secondary: 60F05, 60J80

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 4 • October 2000
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