Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On lower bounds for the L_2-discrepancy   The L_2-discrepancy measures the irregularity of the distribution of a finite
point set. In this note we prove lower bounds for the L_2 discrepancy of
arbitrary N-point sets. Our main focus is on the two-dimensional case.
Asymptotic upper and lower estimates of the L_2-discrepancy in dimension 2 are
well-known and are of the sharp order sqrt(log N). Nevertheless the gap in the
constants between the best known lower and upper bounds is unsatisfactory large
for a two-dimensional problem. Our lower bound improves upon this situation
considerably. The main method is an adaption of the method of K. F. Roth using
the Fourier coefficients of the discrepancy function with respect to the Haar
basis.

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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: eess