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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
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: http://dx.doi.org/10.1090/S1079-6762-98-00046-8
PII: S 1079-6762(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