GAUSSIAN LIMIT FOR CRITICAL ORIENTED PERCOLATION IN HIGH DIMENSIONS

In this paper, we consider the spread-out oriented bond percolation mo dels in Z(d) X Z With d > 4 and the nearest-neighbor oriented bond per colation model in sufficiently high dimensions. Let n(n), n = 1, 2,... , be the random measures defined on R(d) by [GRAPHICS] The mean of eta (n) denoted by <(eta)over bar>(n), is the measure defined by <(eta)ove r bar>(n)(A) = E(p)[eta(n)(A)] We use the lace expansion method to sho w that the sequence of probability measures [<(eta)over bar>(n)(R(d))] (-1)<(eta)over bar>(n) converges weakly to a Gaussian limit as n --> i nfinity for every p in the subcritical regime as well as the critical regime of these percolation models. Also we show that for these models the parallel correlation length xi(p) similar to \p(c) - p\(-1) as p up arrow p(c).