Quantitative form of Ball’s cube slicing in $\mathbb {R}^n$ and equality cases in the min-entropy power inequality
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- by James Melbourne and Cyril Roberto PDF
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Abstract:
We prove a quantitative form of the celebrated Ball’s theorem on cube slicing in $\mathbb {R}^n$ and obtain, as a consequence, equality cases in the min-entropy power inequality. Independently, we also give a quantitative form of Khintchine’s inequality in the special case $p=1$.References
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Additional Information
- James Melbourne
- Affiliation: Centro de Investigación en Matemáticas, Probabilidad y Estadísticas.: 36023 Guanajuato, Gto, Mexico
- MR Author ID: 1138636
- ORCID: 0000-0002-1263-0961
- Email: james.melbourne@cimat.mx
- Cyril Roberto
- Affiliation: Université Paris Nanterre, Modal’X, UMR CNRS 9023, FP2M, CNRS FR 2036, 200 avenue de la République 92000 Nanterre, France
- MR Author ID: 665751
- ORCID: 0000-0003-0522-0101
- Email: croberto@math.cnrs.fr
- Received by editor(s): September 2, 2021
- Received by editor(s) in revised form: October 10, 2021, and November 11, 2021
- Published electronically: May 13, 2022
- Additional Notes: The second author was supported by the Labex MME-DII funded by ANR, reference ANR-11-LBX-0023-01 and ANR-15-CE40-0020-03 - LSD - Large Stochastic Dynamics, and the grant of the Simone and Cino Del Duca Foundation, France.
- Communicated by: Zhen-Qing Chen
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3595-3611
- MSC (2020): Primary 52A40, 52A20, 51M25, 52A38
- DOI: https://doi.org/10.1090/proc/15944
- MathSciNet review: 4439479