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arXiv · 2301.09380

Distributional stability of the Szarek and Ball inequalities

Alexandros Eskenazis·Piotr Nayar·Tomasz Tkocz
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Abstract

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).

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Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz. 2023-01-23. Distributional stability of the Szarek and Ball inequalities. https://doi.org/10.1007/s00208-023-02669-9

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