A Rényi entropy interpretation of anti-concentration and noncentral sections of convex bodies
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912942260224000 |
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| author | Melbourne, James Tkocz, Tomasz Wyczesany, Katarzyna |
| author_facet | Melbourne, James Tkocz, Tomasz Wyczesany, Katarzyna |
| contents | We extend Bobkov and Chistyakov's (2015) upper bounds on concentration functions of sums of independent random variables to a multivariate entropic setting. The approach is based on pointwise estimates on densities of sums of independent random vectors uniform on centred Euclidean balls. In this vein, we also obtain sharp bounds on volumes of noncentral sections of isotropic convex bodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04200 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Rényi entropy interpretation of anti-concentration and noncentral sections of convex bodies Melbourne, James Tkocz, Tomasz Wyczesany, Katarzyna Probability Functional Analysis Metric Geometry We extend Bobkov and Chistyakov's (2015) upper bounds on concentration functions of sums of independent random variables to a multivariate entropic setting. The approach is based on pointwise estimates on densities of sums of independent random vectors uniform on centred Euclidean balls. In this vein, we also obtain sharp bounds on volumes of noncentral sections of isotropic convex bodies. |
| title | A Rényi entropy interpretation of anti-concentration and noncentral sections of convex bodies |
| topic | Probability Functional Analysis Metric Geometry |
| url | https://arxiv.org/abs/2406.04200 |