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- W4301490969 abstract "Let $X$ be a proper geodesic Gromov hyperbolic metric space and let $G$ be a cocompact group of isometries of $X$ admitting a uniform lattice. Let $d$ be the Hausdorff dimension of the Gromov boundary $partial X$. We define the critical exponent $delta(mu)$ of any discrete invariant random subgroup $mu$ of the locally compact group $G$ and show that $delta(mu) > frac{d}{2}$ in general and that $delta(mu) = d$ if $mu$ is of divergence type. Whenever $G$ is a rank-one simple Lie group with Kazhdan's property $(T)$ it follows that an ergodic invariant random subgroup of divergence type is a lattice. One of our main tools is a maximal ergodic theorem for actions of hyperbolic groups due to Bowen and Nevo." @default.
- W4301490969 created "2022-10-05" @default.
- W4301490969 creator A5088517746 @default.
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- W4301490969 date "2018-04-09" @default.
- W4301490969 modified "2023-09-23" @default.
- W4301490969 title "Critical exponents of invariant random subgroups in negative curvature" @default.
- W4301490969 doi "https://doi.org/10.48550/arxiv.1804.02995" @default.
- W4301490969 hasPublicationYear "2018" @default.
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