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arXiv · 1910.11639

Aspects of Convergence of Random Walks on Finite Volume Homogeneous Spaces

Roland Prohaska
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Abstract

We investigate three aspects of weak* convergence of the $n$-step distributions of random walks on finite volume homogeneous spaces $G/\Gamma$ 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.

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Roland Prohaska. 2019-10-25. Aspects of Convergence of Random Walks on Finite Volume Homogeneous Spaces. https://doi.org/10.1080/14689367.2023.2271407

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