시간: 오후 3-4시, 4:30-5:30 (2회)
In this talk, we discuss a relation between two boundaries for a finitely generated group: Martin boundary associated with a finitely supported symmetric random walk, and Floyd boundary obtained from a conformal scaling of Cayley graphs. We prove that the identity map over the group extends to a continuous equivariant surjection from the Martin boundary to the Floyd boundary, with preimages of conical points being singletons. Applications are given to the class of relatively hyperbolic groups. This is joint work with I. Gekhtman, V. Gerasimov and L. Potyagailo.