Self-Avoiding Paths on the Three Dimensional Sierpinski Gasket

Kumiko Hattori, Tetsuya Hattori, Shigeo Kusuoka

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We study self-avoiding paths on the three-dimensional pre-Sierpinski gasket. We prove the existence of the limit distribution of the scaled path length, the exponent for the mean square displacement, and the continuum limit. We also prove that the continuum-limit process is a self-avoiding process on the three-dimensional Sierpinski gasket, and that a path almost surely has infinitely fine creases.

Original languageEnglish
Pages (from-to)455-509
Number of pages55
JournalPublications of the Research Institute for Mathematical Sciences
Volume29
Issue number3
DOIs
Publication statusPublished - 1993
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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