Open Access
August, 1983 The Binary Contact Path Process
David Griffeath
Ann. Probab. 11(3): 692-705 (August, 1983). DOI: 10.1214/aop/1176993514


We study some $\{0, 1, \cdots\}^{z^d}$ valued Markov interactions $\eta_t$ called contact path processes. These are similar to branching random walks, in that the normalized size process starting from a singleton is a martingale which converges to a limit $M_\infty$. In contrast to branching, however, $M_\infty$ depends on the spatial dynamics of the path process. The main result is an exact evaluation of the variance of $M_\infty$, achieved by means of the Feynman-Kac formula. The basic contact process of Harris may be viewed as a projection of $\eta_t$; as a corollary to the main result we obtain bounds on the contact process critical value $\lambda^{(d)}_c$ in dimension $d \geq 3$.


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David Griffeath. "The Binary Contact Path Process." Ann. Probab. 11 (3) 692 - 705, August, 1983.


Published: August, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0524.60096
MathSciNet: MR704556
Digital Object Identifier: 10.1214/aop/1176993514

Primary: 60K35

Keywords: contact processes , critical values , Feynman-Kac formula , interacting particle systems , phase transition

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 3 • August, 1983
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