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arXiv · 2512.09077

Negative Moments of Steinhaus Sums

Martin Rapaport·Tomasz Tkocz·Isabella Wu
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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 $L_p-L_2$ 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.

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Martin Rapaport, Tomasz Tkocz, Isabella Wu. 2025-12-09. Negative Moments of Steinhaus Sums. https://arxiv.org/abs/2512.09077

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