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  1. ; ; (, Mathematische Annalen)
    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). 
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  2. ; ; (, Mathematika)
    Abstract We prove a dimension‐free stability result for polydisc slicing due to Oleszkiewicz and Pełczyński. Intriguingly, compared to the real case, there is an additional asymptotic maximizer. In addition to Fourier‐analytic bounds, we crucially rely on a self‐improving feature of polydisc slicing, established via probabilistic arguments. 
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  3. ; ; (, Duke Mathematical Journal)
    Free, publicly-accessible full text available November 15, 2025
  4. (, Adv. Anal. Geom.)
    Accepted Manuscript Full Text Available