Abstract:We introduce $p$-uniformity to characterize the scaling of density fluctuations in spatial random systems in $\mathbb R^d$, ranging from hyperfluctuation to stealthy hyperuniformity. Our central theorem establishes sufficient conditions to preserve $p$-uniformity under transport. The first condition, a finite $(d+p)$-th moment of the transport distance, allows for a Taylor expansion of the transport. The second condition controls the corresponding terms. We thus solve a previously stated open problem; indeed we extend it, since our result applies to a general $p$-uniform source in any dimension, and the source and transport may be dependent. As an application, we construct new classes of point processes that are isotropic and $p$-uniform with arbitrarily high $p$, and that can be simulated in linear time. We thus achieve three-dimensional isotropic hyperuniform samples with an unprecedented system size of $10^9$ points. We conclude with an outlook on a converse statement.
From: Luca Lotz [view email]
[v1]
Thu, 21 May 2026 17:54:43 UTC (180 KB)
[v2]
Fri, 14 Aug 2026 16:52:45 UTC (790 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。