The incipient infinite cluster in high-dimensional percolation

Authors:
Takashi Hara and Gordon Slade

Journal:
Electron. Res. Announc. Amer. Math. Soc. **4** (1998), 48-55

MSC (1991):
Primary 82B43, 60K35

DOI:
https://doi.org/10.1090/S1079-6762-98-00046-8

Published electronically:
July 31, 1998

MathSciNet review:
1637050

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Abstract: 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.

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Additional Information

**Takashi Hara**

Affiliation:
Department of Applied Physics, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152, Japan

Email:
hara@ap.titech.ac.jp

**Gordon Slade**

Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada L8S 4K1

Email:
slade@mcmaster.ca

DOI:
https://doi.org/10.1090/S1079-6762-98-00046-8

Keywords:
Critical exponent,
incipient infinite cluster,
integrated super-Brownian excursion,
percolation,
scaling limit,
super-Brownian motion

Received by editor(s):
March 17, 1998

Received by editor(s) in revised form:
May 20, 1998

Published electronically:
July 31, 1998

Communicated by:
Klaus Schmidt

Article copyright:
© Copyright 1998
American Mathematical Society