Year: 2026
Type: preprint
Abstract: We prove that the unnormalized discrepancy function of every $n$-point set in the unit square has absolute value at least $c\sqrt{1+\log n}$ on a set of measure at least $η$, with absolute constants $c,η>0$. Consequently, its $L_p$-quasinorm is bounded below by $c\,η^{1/p} \sqrt{1+\log n}$ for every $p>0$.
Source: arXiv (Cornell University)
Author: Hinrichs, Aicke
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223785503