Displacement exponent for loop-erased random walk on the Sierpiński gasket

Kumiko Hattori

Stochastic Processes and their Applications, 2019, vol. 129, issue 11, 4239-4268

Abstract: We prove that loop-erased random walks on the finite pre-Sierpiński gaskets can be extended to a loop-erased random walk on the infinite pre-Sierpiński gasket by using 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: Loop-erased random walk; Displacement exponent; Growth exponent; Law of the iterated logarithm; Sierpiński gasket; Fractal (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.11.021

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