##### Department of Mathematics,

University of California San Diego

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### Math 211B - Group Actions Seminar

## Timothée Bénard

#### Centre for Mathematical Sciences, University of Cambridge

## Random walks with bounded first moment on finite volume spaces

##### Abstract:

We consider a finite volume homogeneous space endowed with a random walk whose driving measure is Zariski-dense. In the case where jumps have finite exponential moment, Eskin-Margulis and Benoist-Quint established recurrence properties for such a walk. I will explain how their results can be extended to walks with finite first moment. The key is to make sense of the following claim: "the walk in a cusp goes down faster that some iid Markov chain on R with negative mean". Joint work with N. de Saxcé.

Host: Brandon Seward

### May 25, 2023

### 10:00 AM

Zoom ID 967 4109 3409 (password: dynamics)

Research Areas

Ergodic Theory and Dynamical Systems****************************