Persistence of asymptotic variance under transport: from hyperfluctuation to stealthy hyperuniformity
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911705434423296 |
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| author | Lotz, Luca Klatt, Michael A. |
| author_facet | Lotz, Luca Klatt, Michael A. |
| contents | 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 conclude with an outlook on a converse statement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22803 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Persistence of asymptotic variance under transport: from hyperfluctuation to stealthy hyperuniformity Lotz, Luca Klatt, Michael A. Probability Disordered Systems and Neural Networks Soft Condensed Matter 60G55, 60G57 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 conclude with an outlook on a converse statement. |
| title | Persistence of asymptotic variance under transport: from hyperfluctuation to stealthy hyperuniformity |
| topic | Probability Disordered Systems and Neural Networks Soft Condensed Matter 60G55, 60G57 |
| url | https://arxiv.org/abs/2605.22803 |