## Bernoulli

• Bernoulli
• Volume 24, Number 3 (2018), 2256-2277.

### Equilibrium of the interface of the grass-bushes-trees process

#### Abstract

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.

#### Article information

Source
Bernoulli, Volume 24, Number 3 (2018), 2256-2277.

Dates
Revised: October 2016
First available in Project Euclid: 2 February 2018

https://projecteuclid.org/euclid.bj/1517540474

Digital Object Identifier
doi:10.3150/17-BEJ927

Mathematical Reviews number (MathSciNet)
MR3757529

Zentralblatt MATH identifier
06839266

#### Citation

Andjel, Enrique; Mountford, Thomas; Valesin, Daniel. Equilibrium of the interface of the grass-bushes-trees process. Bernoulli 24 (2018), no. 3, 2256--2277. doi:10.3150/17-BEJ927. https://projecteuclid.org/euclid.bj/1517540474

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