Aspects of Convergence of Random Walks on Finite Volume Homogeneous Spaces
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866909186065956864 |
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| author | Prohaska, Roland |
| author_facet | Prohaska, Roland |
| contents | We investigate three aspects of weak* convergence of the $n$-step distributions of random walks on finite volume homogeneous spaces $G/Γ$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1910_11639 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Aspects of Convergence of Random Walks on Finite Volume Homogeneous Spaces Prohaska, Roland Dynamical Systems Primary 60B15, Secondary 22F30, 60G50, 22E30 We investigate three aspects of weak* convergence of the $n$-step distributions of random walks on finite volume homogeneous spaces $G/Γ$ 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. |
| title | Aspects of Convergence of Random Walks on Finite Volume Homogeneous Spaces |
| topic | Dynamical Systems Primary 60B15, Secondary 22F30, 60G50, 22E30 |
| url | https://arxiv.org/abs/1910.11639 |