JournalsprimsVol. 29 , No. 3DOI 10.2977/prims/1195167053

Self-avoiding Paths on the Three Dimensional Sierpinski Gasket

  • Kumiko Hattori

    University of Tokyo, Japan
  • Tetsuya Hattori

    Utsunomiya University, Utsunomiya, Tochigi, Japan
  • Shigeo Kusuoka

    Kyoto University, Japan
Self-avoiding Paths on the Three Dimensional Sierpinski Gasket cover

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.