Abstract
In this article we consider the asymptotic behavior of the contact process when the range $M$ goes to $\infty$. We show that if $\lambda$ is the total birth rate from an isolated particle, then the critical value $\lambda_c(M) \rightarrow 1$ as $M \rightarrow \infty$. The rate of convergence depends upon the dimension: $\lambda_c(M) - 1 \approx M^{-2/3}$ in $d = 1, \approx (\log M)/M^2$ in $d = 2$, and $\approx M^{-d}$ in $d \geq 3$.
Citation
M. Bramson. R. Durrett. G. Swindle. "Statistical Mechanics of Crabgrass." Ann. Probab. 17 (2) 444 - 481, April, 1989. https://doi.org/10.1214/aop/1176991410
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