Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear repetitivity beyond abelian groups   We show that linearly repetitive weighted Delone sets in groups of polynomial
growth have a uniquely ergodic hull. This result applies in particular to the
linearly repetitive weighted Delone sets in homogeneous Lie groups constructed
in the companion paper arXiv:2109.15210 using symbolic substitution methods.
More generally, using the quasi-tiling method of Ornstein-Weiss, we establish
unique ergodicity of hulls of weighted Delone sets in amenable unimodular lcsc
groups under a new repetitivity condition which we call tempered repetitivity.
For this purpose, we establish a general sub-additive convergence theorem,
which also has applications concerning the existence of Banach densities and
uniform approximation of the spectral distribution function of finite hopping
range operators on Cayley graphs.

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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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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: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg