Self-avoiding Paths on the Three Dimensional Sierpinski Gasket | Zendy

Kumiko Hattori | Zendy; Tetsuya Hattori | Zendy; Shigeo Kusuoka | Zendy

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Self-avoiding Paths on the Three Dimensional Sierpinski Gasket

Author(s) -

Kumiko Hattori,

Tetsuya Hattori,

Shigeo Kusuoka

Publication year - 1993

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195167053

Subject(s) - sierpinski triangle , mathematics , exponent , limit (mathematics) , gasket , mathematical analysis , fractal , combinatorics , physics , philosophy , linguistics , thermodynamics

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.

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