Math @ Duke

Publications [#243473] of Richard T. Durrett
Papers Published
 Bramson, M; Cox, JT; Durrett, R, A spatial model for the abundance of species,
Annals of Probability, vol. 26 no. 2
(1998),
pp. 658709
(last updated on 2018/07/19)
Abstract: The voter model, with mutations occurring at a positive rate a, has a unique equilibrium distribution. We investigate the logarithms of the relative abundance of species for these distributions in d ≥ 2. We show that, as α → 0, the limiting distribution is right triangular in d = 2 and uniform in d > 3. We also obtain more detailed results for the histograms that biologists use to estimate the underlying density functions.


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