The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion

Takashi Hara, Gordon Slade

研究成果: ジャーナルへの寄稿学術誌査読

40 被引用数 (Scopus)

抄録

For independent nearest-neighbor bond percolation on ℤd with d≫6, we prove that the incipient infinite cluster's two-point function and three-point function converge to those of integrated super-Brownian excursion (ISE) in the scaling limit. The proof is based on an extension of the new expansion for percolation derived in a previous paper, and involves treating the magnetic field as a complex variable. A special case of our result for the two-point function implies that the probability that the cluster of the origin consists of n sites, at the critical point, is given by a multiple of n-3/2, plus an error term of order n-3/2-∈ with ∈>0. This is a strong version of the statement that the critical exponent δ is given by δ= 2.

本文言語英語
ページ(範囲)1244-1293
ページ数50
ジャーナルJournal of Mathematical Physics
41
3
DOI
出版ステータス出版済み - 3月 2000
外部発表はい

!!!All Science Journal Classification (ASJC) codes

  • 統計物理学および非線形物理学
  • 数理物理学

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