An Extension of Kuczeks Argument to Nonnearest Neighbor Contact Processes

The right edge of a nearest neighbor supercritical contact process satisfies a central limit theorem.(8, 9) In this paper, a block construction is created to extend the argument by Kuczek(9) to the nonnearest neighbor case. The proof of the following fact in the nonnearest neighbor case is the key to the extension: There is a positive chance that the rightmost particle at time 0 infects the rightmost particle at every time.