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- W4300786933 abstract "Alexandrov's inequalities imply that for any convex body $A$, the sequence of intrinsic volumes $V_1(A),ldots,V_n(A)$ is non-increasing (when suitably normalized). Milman's random version of Dvoretzky's theorem shows that a large initial segment of this sequence is essentially constant, up to a critical parameter called the Dvoretzky number. We show that this near-constant behavior actually extends further, up to a different parameter associated with $A$. This yields a new quantitative reverse inequality that sits between the approximate reverse Urysohn inequality, due to Figiel--Tomczak-Jaegermann and Pisier, and the sharp reverse Urysohn inequality for zonoids, due to Hug--Schneider. In fact, we study concentration properties of the volume radius and mean width of random projections of $A$ and show how these lead naturally to such reversals." @default.
- W4300786933 created "2022-10-04" @default.
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- W4300786933 date "2017-02-19" @default.
- W4300786933 modified "2023-10-14" @default.
- W4300786933 title "On a quantitative reversal of Alexandrov's inequality" @default.
- W4300786933 doi "https://doi.org/10.48550/arxiv.1702.05762" @default.
- W4300786933 hasPublicationYear "2017" @default.
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