On Convergence of Random Walks on Moduli Space
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866914777962381312 |
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| author | Prohaska, Roland |
| author_facet | Prohaska, Roland |
| contents | The purpose of this note is to establish convergence of random walks on the moduli space of Abelian differentials on compact Riemann surfaces in two different modes: convergence of the $n$-step distributions from almost every starting point in an affine invariant submanifold towards the associated affine invariant measure, and almost sure pathwise equidistribution towards the affine invariant measure on the $SL_2(\mathbb{R})$-orbit closure of an arbitrary starting point. These are analogues to previous results for random walks on homogeneous spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_04083 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On Convergence of Random Walks on Moduli Space Prohaska, Roland Dynamical Systems Probability Primary 60B15, Secondary 32G15, 60G50, 22F10 The purpose of this note is to establish convergence of random walks on the moduli space of Abelian differentials on compact Riemann surfaces in two different modes: convergence of the $n$-step distributions from almost every starting point in an affine invariant submanifold towards the associated affine invariant measure, and almost sure pathwise equidistribution towards the affine invariant measure on the $SL_2(\mathbb{R})$-orbit closure of an arbitrary starting point. These are analogues to previous results for random walks on homogeneous spaces. |
| title | On Convergence of Random Walks on Moduli Space |
| topic | Dynamical Systems Probability Primary 60B15, Secondary 32G15, 60G50, 22F10 |
| url | https://arxiv.org/abs/2102.04083 |