Celebratio Mathematica — Liggett — Complete Bibliography

Complete Bibliography

Works connected to Joseph Clyde Watkins, III

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T. M. Liggett: “Spatially inhomogeneous contact processes,” pp. 105–140 in Spatial stochastic processes. Edited by K. S. Alexander and J. C. Watkins. Progress in Probability 19. Birkäuser (Boston), 1991. A Festschrift in honor of Ted Harris on his seventieth birthday. MR 1144094 Zbl 0747.60096 incollection

A one-dimensional spatially inhomogeneous contact process is a Markov process in \( \{O,1\}^\mathbb{Z} \), where \( \mathbb{Z} \) is the set of integers, which has the following transitions:

\( 1 \to 0 \) at site \( k \) at rate \( \delta(k) \), and
\( 0 \to 1 \) at site \( k \) at rate \( \rho(k)\,\eta(k+1) + \lambda(k)\,\eta(k-1) \),

where \( \delta(k) > 0 \), \( \rho(k)\geq 0 \), \( \lambda(k)\geq 0 \), and \( \eta\in\{O,1\}^\mathbb{Z} \) is the current configuration. If \[ \delta(k)\equiv 1 \quad\text{and}\quad \rho(k)\equiv\eta(k)\equiv\lambda ,\] this is the basic contact process which was first studied by Harris in 1974. If \[ \{(\delta(k),\rho(k),\eta(k))\mid k\in \mathbb{Z}\} \] 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.

Kenneth Sidney Alexander	Related
Theodore Edward Harris	Related
Joseph Clyde Watkins, III	Related