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Extreme $L_p$ discrepancy, numerical integration and the curse of dimensionality
[Submitted on 23 Feb 2026 (v1), last revised 29 May 2026 (this v · 2026-06-01 · via math updates on arXiv.org

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Abstract:The classical notion of extreme $L_p$ discrepancy is a quantitative measure for the irregularity of distribution of finite point sets in the $d$-dimensinal unit cube. In this paper we find a dual integration problem whose worst-case error is exactly the extreme $L_p$ discrepancy of the underlying integration nodes. Studying this integration problem we show that the extreme $L_p$ discrepancy suffers from the curse of dimensionality for all $p \in (1,\infty)$. It is known that the problem is tractable for $p=\infty$; the case $p=1$ stays open.

Submission history

From: Friedrich Pillichshammer [view email]
[v1] Mon, 23 Feb 2026 12:10:43 UTC (463 KB)
[v2] Wed, 25 Feb 2026 08:01:47 UTC (463 KB)
[v3] Fri, 29 May 2026 13:03:07 UTC (465 KB)

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