The incipient infinite cluster in high-dimensional percolation

1998/05/27 by Takashi Hara, Gordon Slade · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP #math.PR #msc:82B43 #msc:60K35

paper · pdf

published as ERA Amer. Math. Soc. 4 (1998), pp.48-55 · AMS-LaTeX, 8 pages, no figures; To appear in Electronic Research Announcements of the AMS, Volume 4, (1998). http://www.ams.org/era/

arxiv created 1998/05/27 · arxiv updated 2009/11/30

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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