Uniform Distributions on p-Balls and the Singular Role of $p=1,2,\infty$ in p-Norm Geometry
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915626217373696 |
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| author | Pinzón, Carlos |
| author_facet | Pinzón, Carlos |
| contents | This paper studies the relationship between volume and surface uniform measures on n-dimensional p-balls under the p-norm. It is proved that for p=1, p=2 and p=infinity, and only for these values of p, radial projection maps a volumetrically uniform distribution to a surface-uniform distribution. Algorithms for uniform sampling on p-balls and p-spheres are provided, together with empirical illustrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13567 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform Distributions on p-Balls and the Singular Role of $p=1,2,\infty$ in p-Norm Geometry Pinzón, Carlos Statistics Theory Cryptography and Security Numerical Analysis This paper studies the relationship between volume and surface uniform measures on n-dimensional p-balls under the p-norm. It is proved that for p=1, p=2 and p=infinity, and only for these values of p, radial projection maps a volumetrically uniform distribution to a surface-uniform distribution. Algorithms for uniform sampling on p-balls and p-spheres are provided, together with empirical illustrations. |
| title | Uniform Distributions on p-Balls and the Singular Role of $p=1,2,\infty$ in p-Norm Geometry |
| topic | Statistics Theory Cryptography and Security Numerical Analysis |
| url | https://arxiv.org/abs/2411.13567 |