Loop-erased random walk on the Sierpinski gasket

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Hattori, Kumiko¹  Mizuno, Michiaki¹ 

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

关键词: Loop-erased random walk;    Scaling limit;    Displacement exponent;    Fractal dimension;    Sierpinski gasket;    Fractal;   

DOI  :  10.1016/j.spa.2013.08.006

来源: Elsevier

【 摘 要 】

In this paper the loop-erased random walk on the finite pre-Sierpinski gasket is studied. It is proved that the scaling limit exists and is a continuous process. It is also shown that the path of the limiting process is almost surely self-avoiding, while having Hausdorff dimension strictly greater than 1. The loop-erasing procedure proposed in this paper is formulated by erasing loops, in a sense, in descending order of size. It enables us to obtain exact recursion relations, making direct use of 'self-similarity' of a fractal structure, instead of the relation to the uniform spanning tree. This procedure is proved to be equivalent to the standard procedure of chronological loop-erasure. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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