Stability of polydisc slicing
Metric Geometry
2025-01-28 v3 Functional Analysis
Probability
Abstract
We prove a dimension-free stability result for polydisc slicing due to Oleszkiewicz and Pelczy\'nski (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.
Cite
@article{arxiv.2303.16896,
title = {Stability of polydisc slicing},
author = {Nathaniel Glover and Tomasz Tkocz and Katarzyna Wyczesany},
journal= {arXiv preprint arXiv:2303.16896},
year = {2025}
}
Comments
Final version, presentation improved. To appear in Mathematika