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). 

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