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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.19089 |
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| _version_ | 1866929293896974336 |
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| author | Bobkov, Sergey G. Duggal, Devraj |
| author_facet | Bobkov, Sergey G. Duggal, Devraj |
| contents | Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the concentration of measure phenomenon, including second order concentration inequalities. A detail account is also given in the case of the circle, with a short overview of Höffding's kernels and covariance identities in the class of periodic functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19089 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spherical Covariance Representations Bobkov, Sergey G. Duggal, Devraj Probability Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the concentration of measure phenomenon, including second order concentration inequalities. A detail account is also given in the case of the circle, with a short overview of Höffding's kernels and covariance identities in the class of periodic functions. |
| title | Spherical Covariance Representations |
| topic | Probability |
| url | https://arxiv.org/abs/2403.19089 |