Math @ Duke

Publications [#243498] of Richard T. Durrett
Papers Published
 Durrett, R; Limic, V, A surprising poisson process arising from a species competition model,
Stochastic Processes and their Applications, vol. 102 no. 2
(2002),
pp. 301309, ISSN 03044149 [doi]
(last updated on 2017/12/15)
Abstract: Motivated by the work of Tilman (Ecology 75 (1994) 2) and May and Nowak (J. Theoret. Biol. 170 (1994) 95) we consider a process in which points are inserted randomly into the unit interval and a new point kills each point to its left independently and with probability a. Intuitively this dynamic will create a negative dependence between the number of points in adjacent intervals. However, we show that the ensemble of points converges to a Poisson process with intensity 1/(a(1  x)), and the number of points at time t grows like (log t)/a. © 2002 Elsevier Science B.V. All rights reserved.


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