Lower Bounds for the Directional Discrepancy with Respect to an Interval of Rotations

Dmitriy Bilyk, Michelle Mastrianni

arxiv（2023）

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摘要

We show that the lower bound for the optimal directional discrepancy with respect to the class of rectangles in ℝ^2 rotated in a restricted interval of directions [-θ ,θ ] with θ < π/4 is of the order at least N^1/5 with a constant depending on θ .

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关键词

Discrepancy,Uniform distribution,Average decay of the Fourier transform

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