Random walk on the incipient infinite cluster for oriented percolation in high dimensions

Martin T. Barlow*, Antal A. Járai, Takashi Kumagai, Gordon Slade

*この研究の対応する著者

研究成果: Article査読

35 被引用数 (Scopus)

抄録

We consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation on ℤd × ℤ+. In dimensions d > 6, we obtain bounds on exit times, transition probabilities, and the range of the random walk, which establish that the spectral dimension of the incipient infinite cluster is frac {4}{3}, and thereby prove a version of the Alexander-Orbach conjecture in this setting. The proof divides into two parts. One part establishes general estimates for simple random walk on an arbitrary infinite random graph, given suitable bounds on volume and effective resistance for the random graph. A second part then provides these bounds on volume and effective resistance for the incipient infinite cluster in dimensions d > 6, by extending results about critical oriented percolation obtained previously via the lace expansion.

本文言語English
ページ(範囲)385-431
ページ数47
ジャーナルCommunications in Mathematical Physics
278
2
DOI
出版ステータスPublished - 2008 3月
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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