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A remark on the isotropy constant of polytopes

Author: David Alonso-Gutiérrez
Journal: Proc. Amer. Math. Soc. 139 (2011), 2565-2569
MSC (2010): Primary 52B99
Published electronically: December 7, 2010
MathSciNet review: 2784825
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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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Additional Information

David Alonso-Gutiérrez
Affiliation: Departmento de Matemáticas, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
Address at time of publication: The Fields Institute for Research in Mathematical Sciences, 222 College Street, Second Floor, Toronto, Ontario M5T 3J1, Canada

Received by editor(s): June 24, 2010
Published electronically: December 7, 2010
Additional Notes: The author was supported by MCYT grants (Spain) MTM2007-61446; DGA E-64
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.