Abstract
Abstract
We prove that the hitting measure is singular with respect to the Lebesgue measure for random walks driven by finitely supported measures on cocompact, hyperelliptic Fuchsian groups. Moreover, the Hausdorff dimension of the hitting measure is strictly less than one. Equivalently, the inequality between entropy and drift is strict. A similar statement is proven for Coxeter groups.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
Reference44 articles.
1. [18] Funar, L. , Lectures on Fuchsian groups and their moduli, lecture notes for the summer school Géométries à courbure négative ou nulle, groupes discrets et rigidités (Institut Fourier Université de Grenoble, June–July 2004).
2. On the displacement of generators of free Fuchsian groups
3. ‘Entropie des groupes de type fini’;Avez;C. R. Acad. Sci. Paris Sér. A-B,1972
4. On the speed of distance-stationary sequences
5. ‘Harmonic measures and Bowen-Margulis measures’;Ledrappier;Israel J. Math.,1990
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献