Group Actions with Hyperbolicity and Measure Rigidity

Effective equidistribution of random walks

31 mai 2024, 11:00

1h

Amphithéâtre Hermite / Darboux (Institut Henri Poincaré)

Orateur

Timothée Bénard (CNRS/Université Sorbonne Paris Nord)

Description

I will explain why a random walk on ${\text{SL}}_2(\mathbb{R})/{\text{SL}}_2(\mathbb{Z})$ equidistributes with an explicit rate toward the Haar measure, provided the walk is not trapped in a finite orbit and the driving measure is supported by algebraic matrices generating a Zariski-dense subgroup. The argument is based on a multislicing theorem which extends Bourgain's projection theorem and presents independent interest. Joint work with Weikun He.