#
Random walks beyond hyperbolic groups

April 11 to April 15, 2022
at the

American Institute of Mathematics,
San Jose, California

organized by

Joseph Maher,
Yulan Qing,
and Giulio Tiozzo

## Original Announcement

This workshop will be devoted to extending results
on random walks known for Lie groups or hyperbolic groups, to the more general
class of groups which have actions on (non-proper) Gromov hyperbolic spaces.
There is a well-developed theory of random walks on word hyperbolic groups,
extending the original development of random walks on Lie groups and their
discrete subgroups. Recently, there has been much work in geometric group
theory studying larger classes of groups which need not be hyperbolic, but act
on (non-proper) hyperbolic spaces. Examples include relatively hyperbolic
groups, acylindrical groups, WPD groups and weakly hyperbolic groups.

The goal of this workshop is to bring together people with expertise in
geometric group theory, ergodic theory, probability and related areas to
develop the theory of random walks on groups of isometries of hyperbolic spaces
and other metric spaces, addressing several open problems.

The main topics for the workshop are:

- Central and local limit theorems
- Green metrics and Poisson Boundaries
- Locally compact groups and the Cremona group

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

A list of open problems.

Workshop Videos

Papers arising from the workshop:

Random walks on groups and superlinear divergent geodesics

by Kunal Chawla, Inhyeok Choi, Vivian He, Kasra Rafi

Random divergence of groups

by Antoine Goldsborough, Alessandro Sisto

Random walk speed is a proper function on Teichmüller space

by Aitor Azemar, Vaibhav Gadre, Sébastien Gouëzel, Thomas Haettel, Pablo Lessa, Caglar Uyanik

The Poisson boundary of hyperbolic groups without moment conditions

by Kunal Chawla, Behrang Forghani, Joshua Frisch, Giulio Tiozzo