##### Department of Mathematics,

University of California San Diego

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### Special Colloquium

## Tianyi Zheng

#### Stanford University

## Random walk parameters and the geometry of groups

##### Abstract:

The first characterization of groups by an asymptotic description of random walks on their Cayley graphs dates back to Kestenâ€™s criterion of amenability. I will first review some connections between the random walk parameters and the geometry of the underlying groups. I will then discuss a flexible construction that gives solution to the inverse problem (given a function, find a corresponding group) for large classes of speed, entropy and return probability of simple random walks on groups of exponential volume growth. Based on joint work with Jeremie Brieussel.

Host: Todd Kemp

### December 4, 2015

### 2:00 PM

### AP&M 6402

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