

02:04:43
published on April 3, 2025
Regularity Theory of Kinetic Equations with Rough Coefficients (3/4)
By Clément Mouhot
Appears in collection : 2024 - T2 - WS2 - Group actions with hyperbolicity and measure rigidity
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.