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arXiv · 1607.04954

Displacement exponent for loop-erased random walk on the Sierpi\'nski gasket

Kumiko Hattori
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Abstract

We prove that loop-erased random walks on finite pre-Sierpinski gaskets can be extended to the infinite pre-Sierpinski gasket by virtue of 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.

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Kumiko Hattori. 2016-07-18. Displacement exponent for loop-erased random walk on the Sierpi\'nski gasket. https://arxiv.org/abs/1607.04954

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