Negative Moments of Steinhaus Sums
Probability
2026-01-01 v2 Functional Analysis
Abstract
We prove a sharp upper bound on negative moments of sums of independent Steinhaus random variables (that is uniform on circles in the plane). Together with the series of earlier works: K\"onig-Kwapie\'n (2001), Baernstein II-Culverhouse (2002), and K\"onig (2014), this closes the investigation of sharp Khinchin-type inequalities for the Steinhaus sums. Incidentally, we fix a mistake in an earlier paper, as well as provide an application to sharp bounds on R\'enyi entropy.
Keywords
Cite
@article{arxiv.2512.09077,
title = {Negative Moments of Steinhaus Sums},
author = {Martin Rapaport and Tomasz Tkocz and Isabella Wu},
journal= {arXiv preprint arXiv:2512.09077},
year = {2026}
}