Random sets are close to low-discrepancy sets

Gleb Smirnov; Roman Vershynin

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arXiv · 2607.12263

Random sets are close to low-discrepancy sets

Gleb Smirnov·Roman Vershynin

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Abstract

We show that a random sample from an arbitrary probability measure on $\mathbb{R}^d$ is close to a low-discrepancy point set. Namely, after moving only a small fraction of the sample points in expectation, one obtains an $n$-point set with star discrepancy $\operatorname{polylog}(n)/n$ with respect to the original measure.

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Gleb Smirnov, Roman Vershynin. 2026-07-14. Random sets are close to low-discrepancy sets. https://arxiv.org/abs/2607.12263

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