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The incipient infinite cluster in high-dimensional percolation
Author(s):
Takashi
Hara;
Gordon
Slade
Journal:
Electron. Res. Announc. Amer. Math. Soc.
4
(1998),
48-55.
MSC (1991):
Primary 82B43, 60K35
Posted:
July 31, 1998
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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:
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
Posted:
July 31, 1998
Communicated by:
Klaus Schmidt
Copyright of article:
Copyright
1998,
American Mathematical Society
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