Self-avoiding process on the Sierpinski gasket

Kumiko Hattori, Tetsuya Hattori

研究成果: Article査読

13 被引用数 (Scopus)

抄録

We construct a self-avoiding process taking values in the finite Sierpinski gasket, and study its properties. We then study "continuum limit" processes that are suggested by the statistical mechanics of self-avoiding paths on the pre-Sierpinski gasket. We prove that there are three types of continuum limit processes according to the parameters defining the statistical mechanics of self-avoiding paths: (i) the self-avoiding process we construct in this paper; (ii) a deterministic motion along a "Peano curve" on the finite Sierpinski gasket; (iii) a deterministic motion along a line segment.

本文言語English
ページ(範囲)405-428
ページ数24
ジャーナルProbability Theory and Related Fields
88
4
DOI
出版ステータスPublished - 1991 12月
外部発表はい

ASJC Scopus subject areas

  • 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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