Loop-erased random walk on the Sierpinski gasket

Kumiko Hattori; Michiaki Mizuno

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arXiv · 1209.4959

Loop-erased random walk on the Sierpinski gasket

Kumiko Hattori·Michiaki Mizuno

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Abstract

We consider a model of loop-erased random walks on the finite pre-Sierpinski gasket which permits rigorous analysis. We prove the existence of the scaling limit and show that the path of the limiting process is almost surely self-avoiding, while having Hausdorff dimension strictly greater than 1. This result means that the path has infinitely fine creases, while having no self-intersection. Our loop-erasing procedure is formulated by a `larger-scale-loops-first' rule. It enables us to obtain exact recursion relations, making use of `self-similarity' of a fractal structure.

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BibTeX RIS

Kumiko Hattori, Michiaki Mizuno. 2012-09-22. Loop-erased random walk on the Sierpinski gasket. https://arxiv.org/abs/1209.4959

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