Loop-erased random walk on the Sierpinski gasket
Probability
2012-09-25 v1
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.
Cite
@article{arxiv.1209.4959,
title = {Loop-erased random walk on the Sierpinski gasket},
author = {Kumiko Hattori and Michiaki Mizuno},
journal= {arXiv preprint arXiv:1209.4959},
year = {2012}
}