分野別セミナー

The long time asymptotics for random walks on infinite graphs is a principal topic in geometry, harmonic analysis, graph theory, to say nothing of probability theory. A covering graph of a finite graph with a nilpotent covering transformation group is called a nilpotent covering graph, regarded as a generalization of a crystal lattice or the Cayley graph of a finite generated group of polynomial volume growth. In this talk, we discuss non-symmetric random walks on nilpotent covering graphs in a point of view of discrete geometric analysis due to Kotani and Sunada, and give a functional central limit theorem for them. We also mention a relationship between the limiting diffusion and distorted Brownian rough paths (discussed in e.g., Bayer-Friz ('13), Friz-Gassiat-Lyons ('15), Chevyrev ('18) and Lopusanschi-Simon ('18)). This talk is based on joint work with Satoshi Ishiwata (Yamagata) and Hiroshi Kawabi (Keio).