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

Given a rooted tree TT in which every vertex has at least one offspring, the harmonic measure for forward moving random walk on the boundary ∂T∂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.