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Haagerup's phase
transition at polydisc slicing
Giorgos Chasapis, Salil Singh and Tomasz Tkocz |
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Vol. 17 (2024), No. 7, 2509–2539
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Abstract |
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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–Pełczyński polydisc slicing result. The Haagerup-type phase transition occurs exactly when the -norm recovers volume, in contrast to the real case. We also obtain partial results in higher dimensions. |
Keywords
polydisc slicing, Bessel function, negative moments,
Khinchin inequality, sharp moment comparison, sums of
independent random vectors, uniform spherically symmetric
random vectors
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Mathematical Subject Classification
Primary: 60E15
Secondary: 33C10, 52A20
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Milestones
Received: 2 June 2022
Revised: 28 November 2022
Accepted: 7 March 2023
Published: 21 August 2024
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Authors |
| Giorgos Chasapis | |
| Department of Mathematics and
Applied Mathematics University of Crete Voutes Campus Crete Greece |
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| Salil Singh | |
| Department of Mathematical
Sciences Carnegie Mellon University Pittsburg, PA United States |
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| Tomasz Tkocz | |
| Department of Mathematical
Sciences Carnegie Mellon University Pittsburgh, PA United States |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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