Haagerup's phase transition at polydisc slicing
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909297701552128 |
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| author | Chasapis, Giorgos Singh, Salil Tkocz, Tomasz |
| author_facet | Chasapis, Giorgos Singh, Salil Tkocz, Tomasz |
| contents | We establish a sharp comparison inequality between the negative moments and the second moment of the magnitude of sums of independent random vectors uniform on three-dimensional Euclidean spheres. This provides a probabilistic extension of the Oleszkiewicz-Pelczyński polydisc slicing result. The Haagerup-type phase transition occurs exactly when the p-norm recovers volume, in contrast to the real case. We also obtain partial results in higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_01026 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Haagerup's phase transition at polydisc slicing Chasapis, Giorgos Singh, Salil Tkocz, Tomasz Probability Functional Analysis Metric Geometry 60E15, 52A20, 33C10 We establish a sharp comparison inequality between the negative moments and the second moment of the magnitude of sums of independent random vectors uniform on three-dimensional Euclidean spheres. This provides a probabilistic extension of the Oleszkiewicz-Pelczyński polydisc slicing result. The Haagerup-type phase transition occurs exactly when the p-norm recovers volume, in contrast to the real case. We also obtain partial results in higher dimensions. |
| title | Haagerup's phase transition at polydisc slicing |
| topic | Probability Functional Analysis Metric Geometry 60E15, 52A20, 33C10 |
| url | https://arxiv.org/abs/2206.01026 |