Negative Moments of Steinhaus Sums
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915700600209408 |
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| author | Rapaport, Martin Tkocz, Tomasz Wu, Isabella |
| author_facet | Rapaport, Martin Tkocz, Tomasz Wu, Isabella |
| contents | 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: König-Kwapień (2001), Baernstein II-Culverhouse (2002), and König (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 Rényi entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09077 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Negative Moments of Steinhaus Sums Rapaport, Martin Tkocz, Tomasz Wu, Isabella Probability Functional Analysis 60E15, 26D15 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: König-Kwapień (2001), Baernstein II-Culverhouse (2002), and König (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 Rényi entropy. |
| title | Negative Moments of Steinhaus Sums |
| topic | Probability Functional Analysis 60E15, 26D15 |
| url | https://arxiv.org/abs/2512.09077 |