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Random walks on vertex-transitive graph with moderate growth

David Guo

University of Bristol

Time: 16:30-18:00 (GMT+8), Monday December 5th, 2022
Location: Zoom

Abstract: We will be looking at the mixing time of symmetric random walks on vertex-transitive graphs. Given a vertex-transitive graph \(G\) with diameter \(\gamma\), Diaconis and Salof-Coste showed that if \(G\) is a Cayley graph of moderate growth then the mixing time of the simple random walk on \(G\) is quadratic in \(\gamma\). The main technique they used was bounding the return probability and the spectral gap of the walk. We will generalise their result to arbitrary finite vertex-transitive graphs, and give an application of this result.

Host: 黄弘毅 Hong Yi Huang