Hyperuniformity of random measures on Euclidean and hyperbolic spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910454439215104 |
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| author | Björklund, Michael Byléhn, Mattias |
| author_facet | Björklund, Michael Byléhn, Mattias |
| contents | We investigate lower asymptotic bounds of number variances for invariant locally square-integrable random measures on Euclidean and real hyperbolic spaces. In the Euclidean case we show that there are subsequences of radii for which the number variance grows at least as fast as the volume of the boundary of Euclidean balls, generalizing a classical result of Beck. With regards to real hyperbolic spaces we prove that random measures are never geometrically hyperuniform and if the random measure admits non-trivial complementary series diffraction, then it is hyperfluctuating. Moreover, we define spectral hyperuniformity and stealth of random measures on real hyperbolic spaces in terms of vanishing of the complementary series diffraction and sub-Poissonian decay of the principal series diffraction around the Harish-Chandra $Ξ$-function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12737 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hyperuniformity of random measures on Euclidean and hyperbolic spaces Björklund, Michael Byléhn, Mattias Probability Classical Analysis and ODEs Dynamical Systems Primary: 60G55. Secondary: 60G57, 43A90 We investigate lower asymptotic bounds of number variances for invariant locally square-integrable random measures on Euclidean and real hyperbolic spaces. In the Euclidean case we show that there are subsequences of radii for which the number variance grows at least as fast as the volume of the boundary of Euclidean balls, generalizing a classical result of Beck. With regards to real hyperbolic spaces we prove that random measures are never geometrically hyperuniform and if the random measure admits non-trivial complementary series diffraction, then it is hyperfluctuating. Moreover, we define spectral hyperuniformity and stealth of random measures on real hyperbolic spaces in terms of vanishing of the complementary series diffraction and sub-Poissonian decay of the principal series diffraction around the Harish-Chandra $Ξ$-function. |
| title | Hyperuniformity of random measures on Euclidean and hyperbolic spaces |
| topic | Probability Classical Analysis and ODEs Dynamical Systems Primary: 60G55. Secondary: 60G57, 43A90 |
| url | https://arxiv.org/abs/2405.12737 |