Distributional stability of the Szarek and Ball inequalities
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917902626586624 |
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| author | Eskenazis, Alexandros Nayar, Piotr Tkocz, Tomasz |
| author_facet | Eskenazis, Alexandros Nayar, Piotr Tkocz, Tomasz |
| contents | We prove an extension of Szarek's optimal Khinchin inequality (1976) for distributions close to the Rademacher one, when all the weights are uniformly bounded by a $1/\sqrt2$ fraction of their total $\ell_2$-mass. We also show a similar extension of the probabilistic formulation of Ball's cube slicing inequality (1986). These results establish the distributional stability of these optimal Khinchin-type inequalities. The underpinning to such estimates is the Fourier-analytic approach going back to Haagerup (1981). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_09380 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Distributional stability of the Szarek and Ball inequalities Eskenazis, Alexandros Nayar, Piotr Tkocz, Tomasz Probability Functional Analysis Metric Geometry 60E15, 42A38, 26D15, 60G50 We prove an extension of Szarek's optimal Khinchin inequality (1976) for distributions close to the Rademacher one, when all the weights are uniformly bounded by a $1/\sqrt2$ fraction of their total $\ell_2$-mass. We also show a similar extension of the probabilistic formulation of Ball's cube slicing inequality (1986). These results establish the distributional stability of these optimal Khinchin-type inequalities. The underpinning to such estimates is the Fourier-analytic approach going back to Haagerup (1981). |
| title | Distributional stability of the Szarek and Ball inequalities |
| topic | Probability Functional Analysis Metric Geometry 60E15, 42A38, 26D15, 60G50 |
| url | https://arxiv.org/abs/2301.09380 |