Abstract
We consider a symmetric finite-range contact process on with two types of particles (or infections), which propagate according to the same supercritical rate and die (or heal) at rate 1. Particles of type 1 can enter any site in that is empty or occupied by a particle of type 2 and, analogously, particles of type 2 can enter any site in that is empty or occupied by a particle of type 1. Also, at most one particle can occupy each site. We prove that the process with initial configuration converges in distribution to an invariant measure different from the non trivial invariant measure of the classic contact process. In addition, we prove that for any initial configuration the process converges to a convex combination of four invariant measures.
Funding Statement
The author was supported by FAPESP grant post doctoral fellowship.
Acknowledgements
The author thanks Majela Pentón Machado for a careful reading of this work and the many constructive suggestions which improved the exposition considerably. The author also thanks Enrique Andjel and Maria Eulalia Vares for the helpful comments during the preparation of this paper.
Citation
Mariela Pentón Machado. "Convergence of the one-dimensional contact process with two types of particles and priority." Bernoulli 29 (2) 1343 - 1367, May 2023. https://doi.org/10.3150/22-BEJ1501
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