Physics – Mathematical Physics
Scientific paper
1999-03-25
J. Math. Phys., 41 (2000) 1244-1293
Physics
Mathematical Physics
56 pages, 3 Postscript figures, in AMS-LaTeX, with graphicx, epic, and xr packages
Scientific paper
10.1063/1.533186
For independent nearest-neighbour 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 statement that the critical exponent delta is given by delta =2.
Hara Takashi
Slade Gordon
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