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Travelling wave structure of the one dimensional contact process

Author

Listed:
  • Galves, A.
  • Presutti, E.

Abstract

We consider the one dimensional supercritical contact process with initial configurations having infinitely many particles to the left of the origin and finitely many ones to its right. We study the space time structure of the process. In particular we prove that the law of the process shifted by [alpha]t (t being the time and [alpha] the drift of the edge) converges weakly to a 4 mixture of the two extremal invariant measures for the supercritical contact process, thus extending a result of [3]. We then show that [even] conditioning on the position of the edge, the distribution of the particles to its left is given by [mu], the unique invariant measure as seen from the edge, cf. [2] and [3]. An interpretation of the above results in terms of a discrete/particle/description of a one dimensional travelling wave is then discussed.

Suggested Citation

  • Galves, A. & Presutti, E., 1987. "Travelling wave structure of the one dimensional contact process," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 153-163.
    • Handle: RePEc:eee:spapps:v:25:y:1987:i::p:153-163
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