## Abstract

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-∈} with ∈>0. This is a strong version of the statement that the critical exponent δ is given by δ= 2.

Original language | English |
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Pages (from-to) | 1244-1293 |

Number of pages | 50 |

Journal | Journal of Mathematical Physics |

Volume | 41 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2000 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics