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

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. W...

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Bibliographic Details
Published in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2018-08, Vol.24 (3), p.2256-2277
Main Authors: ANDJEL, ENRIQUE, MOUNTFORD, THOMAS, VALESIN, DANIEL
Format: Article
Language:English
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Summary: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.
ISSN:1350-7265
DOI:10.3150/17-BEJ927