Stochastic Analysis Seminar
The long time asymptotics for random walks on infinite graphs are principal topics for both geometers and robabilists. A covering graph of a finite graph with a nilpotent covering transformation group is called a nilpotent covering graph, regarded as a generalisation of a crystal Lattice or a Cayley graph of a finitely generated group of polynomial growth.
In this talk, we discuss non-symmetric random walks on nilpotent covering graphs from a view point of discrete geometric analysis developed by Kotani and Sunada. We establish a functional CLT (a generalization of the Donsker-type invariance Principle) for the random walk. Moreover, a relation between the limiting diffusion process and a Brownian rough path with a linear drift is discussed.
This talk is based on joint work with Satoshi Ishiwata (Yamagata University) and Hiroshi Kawabi (Keio University).