Summary
A one-dimensional spatially inhomogeneous contact process is a Markov process in {0, 1}Z, where Z is the set of integers, which has the following transitions:
, where δ(k) < 0, ρ(k) ≥ 0, λ(k) ≥ 0, and η ∈ {0, 1}Z is the current configuration. If δ(k) ≡ 1 and ρ(k) ≡ λ(k) ≡ λ, this is the basic contact process which was first studied by Harris in 1974. If {(δ(k), ρ(k), λ(k)), k ∈ Z} is chosen randomly in a stationary ergodic manner, it is natural to call this a contact process in a random environment. In this paper, we present three types of results, giving sufficient conditions (a) for extinction of the process, (b) for survival of the process, and (c) for the process to have at most four extremal invariant measures.
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© 1991 Springer Science+Business Media New York
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Liggett, T.M. (1991). Spatially Inhomogeneous Contact Processes. In: Alexander, K.S., Watkins, J.C. (eds) Spatial Stochastic Processes. Progress in Probability, vol 19. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0451-0_6
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DOI: https://doi.org/10.1007/978-1-4612-0451-0_6
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