Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The minimal $k$-dispersion of point sets in high-dimensions   In this manuscript we introduce and study an extended version of the minimal
dispersion of point sets, which has recently attracted considerable attention.
Given a set $\mathscr P_n=\{x_1,\dots,x_n\}\subset [0,1]^d$ and
$k\in\{0,1,\dots,n\}$, we define the $k$-dispersion to be the volume of the
largest box amidst a point set containing at most $k$ points. The minimal
$k$-dispersion is then given by the infimum over all possible point sets of
cardinality $n$. We provide both upper and lower bounds for the minimal
$k$-dispersion that coincide with the known bounds for the classical minimal
dispersion for a surprisingly large range of $k$'s.

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The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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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: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph