A surprising poisson process arising from a species competition model


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Durrett, R; Limic, V

Published Date

  • December 1, 2002

Published In

Volume / Issue

  • 102 / 2

Start / End Page

  • 301 - 309

International Standard Serial Number (ISSN)

  • 0304-4149

Digital Object Identifier (DOI)

  • 10.1016/S0304-4149(02)00209-0

Citation Source

  • Scopus