تقرير
On Convergence of Random Walks on Moduli Space
| العنوان: | On Convergence of Random Walks on Moduli Space |
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| المؤلفون: | Prohaska, Roland |
| المصدر: | Illinois J. Math. 65 (2021), pp. 735-747 |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, Mathematics - Probability, Primary 60B15, Secondary 32G15, 60G50, 22F10 |
| الوصف: | 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. Comment: 11 pages; small improvements in presentation in Section 3 on pathwise equidistribution |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1215/00192082-9421088 |
| URL الوصول: | http://arxiv.org/abs/2102.04083 |
| رقم الأكسشن: | edsarx.2102.04083 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1215/00192082-9421088 |
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