On the multifractal analysis of a non-standard branching random walk

Abstract

Consider two branching random walks SnX and \(S_{n}\widetilde{X}\) on a supercritical random Galton–Watson tree. We compute, almost surely and simultaneously, the Hausdorff and packing dimensions of the level set \(E_{X,\widetilde{X}}(a,b)\) of infinite branches in the boundary of the tree along which the averages \(S_{n}X/S_{n}\widetilde{X}\) have a given set of limit points [a,b].