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.
The fundamental inequality for cocompact Fuchsian groups / Kosenko, P.; Tiozzo, G.. - In: FORUM OF MATHEMATICS. SIGMA. - ISSN 2050-5094. - 10:(2022). [10.1017/fms.2022.94]
The fundamental inequality for cocompact Fuchsian groups
Tiozzo G.
2022
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.File allegati a questo prodotto
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