In this paper, we prove that some renowned lower bounds in discrepancy theory admit a discrete analogue. Namely, we prove that the lower bound of the discrepancy for corners in the unit cube due to Roth holds true also for a suitable finite family of corners. We also prove two analogous results for the discrepancy on the torus with respect to squares and balls.

On a Discrete Approach to Lower Bounds in Discrepancy Theory

Gariboldi, Bianca;
2025-01-01

Abstract

In this paper, we prove that some renowned lower bounds in discrepancy theory admit a discrete analogue. Namely, we prove that the lower bound of the discrepancy for corners in the unit cube due to Roth holds true also for a suitable finite family of corners. We also prove two analogous results for the discrepancy on the torus with respect to squares and balls.
2025
Discrepancy
Lower bounds
Irregularities of distribution
Discrete Fourier transform
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12607/79541
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