The incipient infinite cluster in high-dimensional percolation
Mathematical Physics
2007-05-23 v1 math.MP
Probability
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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Cite
@article{arxiv.math-ph/9805023,
title = {The incipient infinite cluster in high-dimensional percolation},
author = {Takashi Hara and Gordon Slade},
journal= {arXiv preprint arXiv:math-ph/9805023},
year = {2007}
}
Comments
AMS-LaTeX, 8 pages, no figures; To appear in Electronic Research Announcements of the AMS, Volume 4, (1998). http://www.ams.org/era/