The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion

For independent nearest-neighbor bond percolation on Z(d) with d > 6, we prove that the incipient infinite cluster's two-point function and three-point function converge to those of integrated super-Brownian excursion (ISE) in the scaling limit. The proof is based on an extension of the new expansion for percolation derived in a previous paper, and involves treating the magnetic field as a complex variable. A special case of our result for the two-point function implies that the probability that the cluster of the origin consists of n sites, at the critical point, is given by a multiple of n(-3/2), plus an error term of order n(-3/2-epsilon) with epsilon > 0. This is a strong version of the statement that the critical exponent delta is given by delta=2. (C) 2000 American Institute of Physics. [S0022-2488(00)00603-4].