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Publications [#243473] of Richard T. Durrett

Papers Published

  1. Bramson, M; Cox, JT; Durrett, R, A spatial model for the abundance of species, Annals of Probability, vol. 26 no. 2 (1998), pp. 658-709
    (last updated on 2017/12/17)

    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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