The Martin boundary of relatively hyperbolic groups with virtually abelian parabolic subgroups

Given a probability measure on finitely generated group, its Martin boundary is way to compactify the group using Green's function of corresponding random walk. We give complete topological characterization supported walks relatively hyperbolic groups with virtually abelian parabolic subgroups. In particular, in case nonuniform lattices real space H n , we show that coincides CAT (0) truncated space, and thus when = 3, homeomorphic Sierpinski carpet.