Aspects of Convergence of Random Walks on Finite Volume Homogeneous Spaces
arXiv:1910.11639 · doi:10.1080/14689367.2023.2271407
Abstract
We investigate three aspects of weak* convergence of the -step distributions of random walks on finite volume homogeneous spaces of semisimple real Lie groups. First, we look into the obvious obstruction to the upgrade from Cesaro to non-averaged convergence: periodicity. We give examples where it occurs and conditions under which it does not. In a second part, we prove convergence towards Haar measure with exponential speed from almost every starting point. Finally, we establish a strong uniformity property for the Cesaro convergence towards Haar measure for uniquely ergodic random walks.
21 pages; improved the speed of convergence in Theorems 3.2 and 3.13 based on referee reports, other minor improvements. The Version of Record of this manuscript has been published and is freely available in Dynamical Systems, 24 Oct 2023, https://www.tandfonline.com/10.1080/14689367.2023.2271407