Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Spherical Cap Discrepancy of HEALPix Points   In this paper we show that the spherical cap discrepancy of the point set
given by centers of pixels in the HEALPix tessellation (short for Hierarchical,
Equal Area and iso-Latitude Pixelation) of unit $2$-sphere is lower and upper
bounded by order square root of the number of points, and compute explicit
constants. This adds to the known collection of explicitly constructed sets
whose discrepancy converges with order $N^{-1/2}$, matching the asymptotic
order for i.i.d. random point sets. We describe the HEALPix framework in more
detail and give explicit formulas for the boundaries and pixel centers. We then
introduce the notion of an $n$-convex curve and prove an upper bound on how
many fundamental domains are intersected by such curves, and in particular we
show that boundaries of spherical caps have this property. Lastly, we mention
briefly that a jittered sampling technique works in the HEALPix framework as
well.

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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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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: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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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: hep-lat