Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical exponents of invariant random subgroups in negative curvature   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.

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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: econ