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We announce our recent proof that, for independent bond percolation in high dimensions, the scaling limits of the incipient infinite cluster's two-point and three-point functions are those of integrated super-Brownian excursion (ISE). The proof uses an extension of the lace expansion for percolation.

Copyright 1998 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 04 (1998), pp. 48-55
• Publisher Identifier: S 1079-6762(98)00046-8
• 1991 Mathematics Subject Classification. Primary 82B43
• Key words and phrases. Critical exponent, incipient infinite cluster, integrated super-Brownian excursion, percolation, scaling limit, super-Brownian motion
• Received by the editors March 17, 1998 and, in revised form, May 20, 1998
• Posted on July 31, 1998
• Communicated by Klaus Schmidt
• Comments (When Available)

Takashi Hara

Department of Applied Physics, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku,

Tokyo 152, Japan

E-mail address: hara@ap.titech.ac.jp

Gordon Slade

Department of Mathematics and Statistics, McMaster University,

Hamilton, ON, Canada L8S 4K1

E-mail address: slade@mcmaster.ca