Abstract
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 $d \geq 3$.
Citation
David Griffeath. "The Binary Contact Path Process." Ann. Probab. 11 (3) 692 - 705, August, 1983. https://doi.org/10.1214/aop/1176993514
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