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 ...

We prove the convex combination theorem for hyperbolic n-manifolds. Many applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, there are finite index subgroups which generated a subgroup that is an am...

We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic nspace, satisfying a natural condition on their parabolic subgroups, there are finite index subgroups which generate a subgroup that is an amalgamat...

We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, and whose intersection is a separable subgroup, there are finite index subgrou...