The multifractal spectrum of harmonic measure for forward moving random walks on a Galton-Watson tree

Adam L. Kinnison

Statistics & Probability Letters, 2008, vol. 78, issue 17, 3114-3121

Abstract: Given a rooted tree T in which every vertex has at least one offspring, the harmonic measure for forward moving random walk on the boundary [not partial differential]T is defined as the distribution of the path of a random particle starting at the root and moving, independently at each time step, to a randomly picked child of the current vertex. We show that the harmonic measure for forward moving random walk is multifractal and determine its multifractal spectrum.

Date: 2008
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