A remark on the isotropy constant of polytopes

Alonso-Gutiérrez, David

doi:10.1090/S0002-9939-2010-10669-X

A remark on the isotropy constant of polytopes
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Proc. Amer. Math. Soc. 139 (2011), 2565-2569 Request permission

Abstract:

It is known that the isotropy constant of any symmetric polytope with $2N$ vertices is bounded by $C\log N$. We give a different proof of this result, which shows that the same estimate is true when the polytope is non-symmetric with $N$ vertices. We also make a remark on how an estimate of the isotropy constant of a symmetric polytope with $2N$ facets of the order of $\sqrt {\log \frac {N}{n}}$, which can be easily deduced from known results, is also true for non-symmetric polytopes with $N$ facets.

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