Haagerup's phase transition at polydisc slicing
Probability
2024-08-28 v2 Functional Analysis
Metric Geometry
Abstract
We establish a sharp comparison inequality between the negative moments and the second moment of the magnitude of sums of independent random vectors uniform on three-dimensional Euclidean spheres. This provides a probabilistic extension of the Oleszkiewicz-Pelczy\'nski polydisc slicing result. The Haagerup-type phase transition occurs exactly when the p-norm recovers volume, in contrast to the real case. We also obtain partial results in higher dimensions.
Cite
@article{arxiv.2206.01026,
title = {Haagerup's phase transition at polydisc slicing},
author = {Giorgos Chasapis and Salil Singh and Tomasz Tkocz},
journal= {arXiv preprint arXiv:2206.01026},
year = {2024}
}
Comments
Final version. To appear in Analysis & PDE