TY - JOUR
T1 - Self-Avoiding Paths on the Three Dimensional Sierpinski Gasket
AU - Hattori, Kumiko
AU - Hattori, Tetsuya
AU - Kusuoka, Shigeo
PY - 1993
Y1 - 1993
N2 - 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.
AB - 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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U2 - 10.2977/prims/1195167053
DO - 10.2977/prims/1195167053
M3 - Article
AN - SCOPUS:85008045036
SN - 0034-5318
VL - 29
SP - 455
EP - 509
JO - Publications of the Research Institute for Mathematical Sciences
JF - Publications of the Research Institute for Mathematical Sciences
IS - 3
ER -