##### Department of Mathematics,

University of California San Diego

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### Probability Seminar

## Tianyi Zheng

#### Stanford University

## Random walks and isoperimetric profiles of groups

##### Abstract:

Asymptotic behavior of random walks on a group, such as decay of return probability and growth of entropy, reflects large scale geometry of the underlying group. The notion of isoperimetric profiles, motivated by classical isoperimetric inequalities and Faber-Krahn inequalities, captures useful geometric information that affects behavior of random walks. In this talk I will explain some interesting examples of groups acting on trees, where random walks exhibit rich exotic behavior. A connection between return probability lower bound and entropy growth will also be discussed.

Host: Ruth Williams

### April 30, 2015

### 10:00 AM

### AP&M 6402

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