Distributional stability of the Szarek and Ball inequalities
| Autor: | Eskenazis, Alexandros, Nayar, Piotr, Tkocz, Tomasz |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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). Comment: Final version. To appear in Math. Ann |
| Databáze: | arXiv |
| Externí odkaz: |
|