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The incipient infinite cluster in high-dimensional percolation
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## The incipient infinite cluster in high-dimensional percolation

### Takashi Hara and Gordon Slade

**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.

*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`

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