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Extremal cross-polytopes and Gaussian vectors
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Gergely Ambrus
Published/Copyright:
January 14, 2015
Abstract
For n ≥ 1, let ξ1, ..., ξn be independent, identically distributed standard normal variables. Among nonnegative real vectors u = (u1, . . . , un) of Euclidean norm 1, the quantity E∥(u1ξ1,..., unξn∥∞ is maximised when u has at most two non-zero entries, and it is minimised when u is proportional to (1,...,1). Further generalisations of this result are also discussed. As a corollary, a lower bound on the mean width of a general convex body K is derived in terms of the successive inner radii of K.
Keywords : Orthogonal crosspolytopes; Gaussian vectors
Received: 2013-2-7
Revised: 2013-6-21
Published Online: 2015-1-14
Published in Print: 2015-1-1
© 2015 by Walter de Gruyter Berlin/Boston
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- Bianchi surfaces whose asymptotic lines are geodesic parallels
- Results on coupled Ricci and harmonic map flows
- Mostow’s lattices and cone metrics on the sphere
- Monads for framed sheaves on Hirzebruch surfaces
- The topology of the minimal regular covers of the Archimedean tessellations
- Extremal cross-polytopes and Gaussian vectors
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Articles in the same Issue
- Frontmatter
- Bianchi surfaces whose asymptotic lines are geodesic parallels
- Results on coupled Ricci and harmonic map flows
- Mostow’s lattices and cone metrics on the sphere
- Monads for framed sheaves on Hirzebruch surfaces
- The topology of the minimal regular covers of the Archimedean tessellations
- Extremal cross-polytopes and Gaussian vectors
- Displacing (Lagrangian) submanifolds in the manifolds of full flags
- The harmonic mean measure of symmetry for convex bodies
- Geodesic vectors and subalgebras in two-step nilpotent metric Lie algebras
- The periods of the generalized Jacobian of a complex elliptic curve
