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arXiv · 2312.10668

On a discrete approach to lower bounds in discrepancy theory

Luca Brandolini·Bianca Gariboldi·Giacomo Gigante·Alessandro Monguzzi
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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.

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Luca Brandolini, Bianca Gariboldi, Giacomo Gigante, Alessandro Monguzzi. 2023-12-17. On a discrete approach to lower bounds in discrepancy theory. https://arxiv.org/abs/2312.10668

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