Stability of polydisc slicing

Abstract

We prove a dimension-free stability result for polydisc slicing due to Oleszkiewicz and Pelczyński (2000). Intriguingly, compared to the real case, there is an additional asymptotic maximiser. In addition to Fourier-analytic bounds, we crucially rely on a self-improving feature of polydisc slicing, established via probabilistic arguments.

Final version, presentation improved. To appear in Mathematika