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April 1998 A spatial model for the abundance of species
Maury Bramson, J. Theodore Cox, Richard Durrett
Ann. Probab. 26(2): 658-709 (April 1998). DOI: 10.1214/aop/1022855647

Abstract

The voter model, with mutations occurring at a positive rate $\alpha$, has a unique equilibrium distribution. We investigate the logarithms of the relative abundance of species for these distributions in $d \geq 2$. We show that, as $\alpha \to \infty$, the limiting distribution is right triangular in $d = 2$ and uniform in $d \geq 3$. We also obtain more detailed results for the histograms that biologists use to estimate the underlying density functions.

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Maury Bramson. J. Theodore Cox. Richard Durrett. "A spatial model for the abundance of species." Ann. Probab. 26 (2) 658 - 709, April 1998. https://doi.org/10.1214/aop/1022855647

Information

Published: April 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0935.60100
MathSciNet: MR1626495
Digital Object Identifier: 10.1214/aop/1022855647

Subjects:
Primary: 60K35, 92D25

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 2 • April 1998
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