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

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.

21pages 5figures. arXiv admin note: text overlap with arXiv:1511.04840

References in corpus (1)

• A family of self-avoiding random walks interpolating the loop-erased random walk and a self-avoiding walk on the Sierpinski gasket