Mean-field critical behaviour for correlation length for percolation in high dimensions

研究成果: Contribution to journalArticle査読

18 被引用数 (Scopus)

抄録

Extending the method of [27], we prove that the corrlation length ξ of independent bond percolation models exhibits mean-field type critical behaviour (i.e. ξ(p∼(pc-p)-1/2 as p↗pc) in two situations: i) for nearest-neighbour independent bond percolation models on a d-dimensional hypercubic lattice ℤd, with d sufficiently large, and ii) for a class of "spread-out" independent bond percolation models, which are believed to belong to the same universality class as the nearest-neighbour model, in more than six dimensions. The proof is based on, and extends, a method developed in [27], where it was used to prove the triangle condition and hence mean-field behaviour of the critical exponents γ, β, δ, Δ and ν2 for the above two cases.

本文言語英語
ページ(範囲)337-385
ページ数49
ジャーナルProbability Theory and Related Fields
86
3
DOI
出版ステータス出版済み - 9 1 1990
外部発表はい

All Science Journal Classification (ASJC) codes

  • 分析
  • 統計学および確率
  • 統計学、確率および不確実性

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