# 群与图讨论班 Seminars on Groups and Graphs

You are here: Seminars > 2022 > December 5th

# 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

Slides