An extension of Kuczek's argument to nonnearest neighbor contact processes

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