Compact doubling spaces as Martin boundaries
As mentioned in the firrst talk, a compact quasi-metric space K is equivalent to the boundary \partial X of some hyperbolic graph X, and the doubling property of K allows X to have bounded degree. In this talk we introduce a class of transient reversible random walks on X such that their Martin boundaries can be identified with K via \partial X. Using Silverstein's theory of Markov chains, we obtain precise estimates of the Martin kernel and the Naim kernel, and prove that the random walk induces an energy form on K with a Besov-type domain. This is a joint work with Ka-Sing Lau and Ting-Kam Leonard Wong.