Hyperuniformity and optimal transport of point processes
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912832324370432 |
|---|---|
| author | Lachièze-Rey, Raphaël Yogeshwaran, D. |
| author_facet | Lachièze-Rey, Raphaël Yogeshwaran, D. |
| contents | We examine optimal matchings or transport between two stationary random measures. It covers allocation from the Lebesgue measure to a point process and matching a point process to a regular (shifted) lattice. The main focus of the article is the impact of hyperuniformity(reduced variance fluctuations in point processes) to optimal transport: in dimension 2, we show that the typical matching cost has finite second moment under a mild logarithmic integrability condition on the reduced pair correlation measure, showing that most planar hyperuniform point processes are L2-perturbed lattices. Our method also retrieves known sharp bounds in finite windows for neutral integrable systems such as Poisson processes, and also applies to hyperfluctuating systems. Further, in three dimensions onwards, all point processes with an integrable pair correlation measure are L2-perturbed lattices without requiring hyperuniformity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13705 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hyperuniformity and optimal transport of point processes Lachièze-Rey, Raphaël Yogeshwaran, D. Probability Mathematical Physics 60G55, 49Q22, 60D05, 60B15, 42A38 We examine optimal matchings or transport between two stationary random measures. It covers allocation from the Lebesgue measure to a point process and matching a point process to a regular (shifted) lattice. The main focus of the article is the impact of hyperuniformity(reduced variance fluctuations in point processes) to optimal transport: in dimension 2, we show that the typical matching cost has finite second moment under a mild logarithmic integrability condition on the reduced pair correlation measure, showing that most planar hyperuniform point processes are L2-perturbed lattices. Our method also retrieves known sharp bounds in finite windows for neutral integrable systems such as Poisson processes, and also applies to hyperfluctuating systems. Further, in three dimensions onwards, all point processes with an integrable pair correlation measure are L2-perturbed lattices without requiring hyperuniformity. |
| title | Hyperuniformity and optimal transport of point processes |
| topic | Probability Mathematical Physics 60G55, 49Q22, 60D05, 60B15, 42A38 |
| url | https://arxiv.org/abs/2402.13705 |