Displacement exponent for loop-erased random walk on the Sierpi\'nski gasket
Probability
2016-07-19 v1
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.
Keywords
Cite
@article{arxiv.1607.04954,
title = {Displacement exponent for loop-erased random walk on the Sierpi\'nski gasket},
author = {Kumiko Hattori},
journal= {arXiv preprint arXiv:1607.04954},
year = {2016}
}
Comments
21pages 5figures. arXiv admin note: text overlap with arXiv:1511.04840