The triangle condition for percolation

Takashi Hara, Gordon Slade

研究成果: ジャーナルへの寄稿記事

4 引用 (Scopus)

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Aizenman and Newman introduced an unverified condition, the triangle condition, which has been shown to imply that a number of percolation critical exponents take their mean field values, and which is expected to hold above six dimensions for nearest neighbour percolation. We prove that the triangle condition is satisfied in sufficiently high dimensions for the nearest neighbour model, and above six dimensions for a class of “spread-out” models. The proof uses an expansion which is related to the lace expansion for self-avoiding walk.

元の言語英語
ページ(範囲)269-273
ページ数5
ジャーナルBulletin of the American Mathematical Society
21
発行部数2
DOI
出版物ステータス出版済み - 10 1989
外部発表Yes

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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