Report
The fundamental inequality for cocompact Fuchsian groups
| العنوان: | The fundamental inequality for cocompact Fuchsian groups |
|---|---|
| المؤلفون: | Kosenko, Petr, Tiozzo, Giulio |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, Mathematics - Geometric Topology, Mathematics - Probability, 60G50, 20F67 (Primary) 30F35, 60J50 (Secondary) |
| الوصف: | We prove that the hitting measure is singular with respect to Lebesgue measure for any random walk on a cocompact Fuchsian group generated by translations joining opposite sides of a symmetric hyperbolic polygon. Moreover, the Hausdorff dimension of the hitting measure is strictly less than 1. A similar statement is proven for Coxeter groups. Along the way, we prove for cocompact Fuchsian groups a purely geometric inequality for geodesic lengths, strongly reminiscent of the Anderson-Canary-Culler-Shalen inequality for free Kleinian groups. Comment: 20 pages, 5 figures. Main result (Theorem 1) strengthened; results on Coxeter groups (Theorem 2) and Hausdorff dimension (Corollary 3) added. Introduction expanded |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2012.07417 |
| رقم الانضمام: | edsarx.2012.07417 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |