Open Access
August 2018 Equilibrium of the interface of the grass-bushes-trees process
Enrique Andjel, Thomas Mountford, Daniel Valesin
Bernoulli 24(3): 2256-2277 (August 2018). DOI: 10.3150/17-BEJ927


We consider the grass-bushes-trees process, which is a two-type contact process in which one of the types is dominant. Individuals of the dominant type can give birth on empty sites and sites occupied by non-dominant individuals, whereas non-dominant individuals can only give birth at empty sites. We study the shifted version of this process so that it is ‘seen from the rightmost dominant individual’ (which is well defined if the process occurs in an appropriate subset of the configuration space); we call this shifted process the grass-bushes-trees interface (GBTI) process. The set of stationary distributions of the GBTI process is fully characterized, and precise conditions for convergence to these distributions are given.


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Enrique Andjel. Thomas Mountford. Daniel Valesin. "Equilibrium of the interface of the grass-bushes-trees process." Bernoulli 24 (3) 2256 - 2277, August 2018.


Received: 1 May 2016; Revised: 1 October 2016; Published: August 2018
First available in Project Euclid: 2 February 2018

zbMATH: 06839266
MathSciNet: MR3757529
Digital Object Identifier: 10.3150/17-BEJ927

Keywords: contact process , interacting particle systems

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 3 • August 2018
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