Hyperuniform random measures, transport and rigidity
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918164734935040 |
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| author | Lachièze-Rey, Raphaël |
| author_facet | Lachièze-Rey, Raphaël |
| contents | This survey explores the foundational theory and recent developments in the study of hyperuniformity. We present a comprehensive mathematical framework in the context of weakly stationary random measures, emphasizing spectral characterizations and second order asymptotics. Classical examples - including determinantal point processes, Gibbs measures, and zero sets of Gaussian analytic functions - are presented in depth to illustrate core principles. We also highlight recent progress connecting hyperuniformity with optimal transport and rigidity phenomena, pointing to emerging directions in the field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18392 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperuniform random measures, transport and rigidity Lachièze-Rey, Raphaël Probability This survey explores the foundational theory and recent developments in the study of hyperuniformity. We present a comprehensive mathematical framework in the context of weakly stationary random measures, emphasizing spectral characterizations and second order asymptotics. Classical examples - including determinantal point processes, Gibbs measures, and zero sets of Gaussian analytic functions - are presented in depth to illustrate core principles. We also highlight recent progress connecting hyperuniformity with optimal transport and rigidity phenomena, pointing to emerging directions in the field. |
| title | Hyperuniform random measures, transport and rigidity |
| topic | Probability |
| url | https://arxiv.org/abs/2510.18392 |