分野別セミナー

Abstract:
Kigami showed that a transient random walk on a deterministic infinite tree T induces its trace process on the Martin boundary of T. In this paper, we will deal with trace processes on Martin boundaries of random trees instead of deterministic ones, and prove short time log-asymptotic of on-diagonal heat kernel estimates and estimates of mean displacements. The ergodic theory of Galton-Watson trees developed by Lyons, Pemantle and Peres plays an important role in this study.