Displacement exponent for loop-erased random walk on the Sierpinski gasket

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Hattori, Kumiko¹ 

[1] Tokyo Metropolitan Univ, Dept Math Sci, Hachioji, Tokyo 1920397, Japan

关键词: Loop-erased random walk;    Displacement exponent;    Growth exponent;    Law of the iterated logarithm;    Sierpinski gasket;    Fractal;   

DOI  :  10.1016/j.spa.2018.11.021

来源: Elsevier

【 摘 要 】

We prove that loop-erased random walks on the finite pre-Sierpinski gaskets can be extended to a loop-erased random walk on the infinite pre-Sierpinski gasket by using the 'erasing-larger-loops-first' method, and obtain the asymptotic behavior of the walk as the number of steps increases, in particular, the displacement exponent and a law of the iterated logarithm. (C) 2018 Published by Elsevier B.V.

【 授权许可】

Free