Self-avoiding process on the Sierpinski gasket

Kumiko Hattori, Tetsuya Hattori

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)405-428
Number of pages24
JournalProbability Theory and Related Fields
Volume88
Issue number4
DOIs
Publication statusPublished - 1991 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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