Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Circle discrepancy for checkerboard measures   Consider the plane as a union of congruent unit squares in a checkerboard
pattern, each square colored black or white in an arbitrary manner. The
discrepancy of a curve with respect to a given coloring is the difference of
its white length minus its black length, in absolute value. We show that for
every radius t>1 there exists a full circle of radius either t or 2t with
discrepancy greater than ct^(1/2) for some numerical constant c>0. We also show
that for every t>1 there exists a circular arc of radius exactly t with
discrepancy greater than ct^(1/2). Finally we investigate the corresponding
problem for more general curves and their interiors. These results answer
questions posed by Kolountzakis and Iosevich.

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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio