Statistical Mechanics of Crabgrass

Bramson, M. ; Durrett, R. ; Swindle, G.

Ann. Probab., Tome 17 (1989) no. 4, p. 444-481 / Harvested from Project Euclid

Résumé

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 $d \geq 3$.

Détail

Publié le : 1989-04-14
Classification:  Contact process,  renormalized bond construction,  branching processes,  60K35,  60J80