A method for finding bounds on critical values for non-attractive interacting particle systems

摘要

The method is to use a computer to find a function for the process that always has negative expectation by considering all relevant configurations of 0's and 1's at the boundary of a finite process in one dimension. It is shown that a branching annihilating random walk will die out if the diffusion parameter rho is greater than 0.176. The method may also be applied to attractive processes, and is used for the contact process in one dimension obtaining the same values as Ziezold and Grillenberger (1988) for up to 10 places in from the boundaries. [References: 11]