Slicing \(\ell_p\)-balls reloaded: stability, planar sections in \(\ell_1\)
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Slicing \(\ell p\)-balls reloaded: stability, planar sections in \(\ell 1\)
Slicing \(\ell p\)-balls reloaded: stability, planar sections in \(\ell 1\)
DOI10.1214/22-AOP1584zbMATH Open1506.52003arXiv2109.05645MaRDI QIDQ2087393
Author name not available (Why is that?)
Publication date: 27 October 2022
Published in: (Search for Journal in Brave)
Abstract: We show that the two-dimensional minimum-volume central section of the -dimensional cross-polytope is attained by the regular -gon. We establish stability-type results for hyperplane sections of -balls in all the cases where the extremisers are known. Our methods are mainly probabilistic, exploring connections between negative moments of projections of random vectors uniformly distributed on convex bodies and volume of their sections.
Full work available at URL: https://arxiv.org/abs/2109.05645
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