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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.10175 |
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| _version_ | 1866909610978312192 |
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| author | Mattesini, Francesco Otto, Felix |
| author_facet | Mattesini, Francesco Otto, Felix |
| contents | The optimal matching of point clouds in $\mathbb{R}^d$ is a combinatorial problem; applications in statistics motivate to consider random point clouds, like the Poisson point process. There is a crucial dependance on dimension $d$, with $d=2$ being the critical dimension. This is revealed by adopting an analytical perspective, connecting e.\,g.~to Optimal Transportation. These short notes provide an introduction to the subject. The material presented here is based on a series of lectures held at the International Max Planck Research School during the summer semester 2022. Recordings of the lectures are available at https://www.mis.mpg.de/events/event/imprs-ringvorlesung-summer-semester-2022. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10175 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Combinatorics to Partial Differential Equations Mattesini, Francesco Otto, Felix Probability The optimal matching of point clouds in $\mathbb{R}^d$ is a combinatorial problem; applications in statistics motivate to consider random point clouds, like the Poisson point process. There is a crucial dependance on dimension $d$, with $d=2$ being the critical dimension. This is revealed by adopting an analytical perspective, connecting e.\,g.~to Optimal Transportation. These short notes provide an introduction to the subject. The material presented here is based on a series of lectures held at the International Max Planck Research School during the summer semester 2022. Recordings of the lectures are available at https://www.mis.mpg.de/events/event/imprs-ringvorlesung-summer-semester-2022. |
| title | From Combinatorics to Partial Differential Equations |
| topic | Probability |
| url | https://arxiv.org/abs/2505.10175 |