Loop-erased random walk on the Sierpinski gasket

Kumiko Hattori and Michiaki Mizuno

Stochastic Processes and their Applications, 2014, vol. 124, issue 1, 566-585

Abstract: In this paper the loop-erased random walk on the finite pre-Sierpiński 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.

Keywords: Loop-erased random walk; Scaling limit; Displacement exponent; Fractal dimension; Sierpinski gasket; Fractal (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2013.08.006

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