Publications [#243498] of Richard T. Durrett

Papers Published

1. Durrett, R; Limic, V, A surprising poisson process arising from a species competition model, Stochastic Processes and their Applications, vol. 102 no. 2 (December, 2002), pp. 301-309, Elsevier BV, ISSN 0304-4149 [doi]
   (last updated on 2024/04/24)

   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.