Distributional stability of the Szarek and Ball inequalities
Résumé
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 $$1/\sqrt{2}$$ 1 / 2 fraction of their total $$\ell _2$$ ℓ 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).
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)