The Extreme Points of Fusions
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866910819650895872 |
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| author | Kleiner, Andreas Moldovanu, Benny Strack, Philipp Whitmeyer, Mark |
| author_facet | Kleiner, Andreas Moldovanu, Benny Strack, Philipp Whitmeyer, Mark |
| contents | Our work explores fusions, the multidimensional counterparts of mean-preserving contractions and their extreme and exposed points. We reveal an elegant geometric/combinatorial structure for these objects. Of particular note is the connection between Lipschitz-exposed points (measures that are unique optimizers of Lipschitz-continuous objectives) and power diagrams, which are divisions of a space into convex polyhedral ``cells'' according to a weighted proximity criterion. These objects are frequently seen in nature--in cell structures in biological systems, crystal and plant growth patterns, and territorial division in animal habitats--and, as we show, provide the essential structure of Lipschitz-exposed fusions. We apply our results to several questions concerning categorization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10779 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Extreme Points of Fusions Kleiner, Andreas Moldovanu, Benny Strack, Philipp Whitmeyer, Mark Theoretical Economics Probability Our work explores fusions, the multidimensional counterparts of mean-preserving contractions and their extreme and exposed points. We reveal an elegant geometric/combinatorial structure for these objects. Of particular note is the connection between Lipschitz-exposed points (measures that are unique optimizers of Lipschitz-continuous objectives) and power diagrams, which are divisions of a space into convex polyhedral ``cells'' according to a weighted proximity criterion. These objects are frequently seen in nature--in cell structures in biological systems, crystal and plant growth patterns, and territorial division in animal habitats--and, as we show, provide the essential structure of Lipschitz-exposed fusions. We apply our results to several questions concerning categorization. |
| title | The Extreme Points of Fusions |
| topic | Theoretical Economics Probability |
| url | https://arxiv.org/abs/2409.10779 |