2020/11/04 by Mariela Pentón Machado, Machado, Mariela Pentón
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2011.02374
We consider a symmetric finite-range contact process on \ℤ with two\ntypes of particles (or infections), which propagate according to the same\nsupercritical rate and die (or heal) at rate 1. Particles of type 1 can\nenter any site in (-\∞,0] that is empty or occupied by a particle of type\n2 and, analogously, particles of type 2 can enter any site in [1,\∞)\nthat is empty or occupied by a particle of type 1. Also, almost one particle\ncan occupy each site. We prove that the process beginning with all sites in\n(-\∞,0] occupied by particles of type 1 and all sites in [1,\∞)\noccupied by particles of type 2 converges in distribution to an invariant\nmeasure different from the nontrivial invariant measure of the classic contact\nprocess. In addition, we prove that for any initial configuration the process\nconverges to a convex combination of four invariant measures.\n