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Remarks on the geometry of coordinate projections in R^n

S. Mendelson·R. Vershynin
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Abstract

We study geometric properties of coordinate projections. Among other results, we show that if a body K in R^n has an "almost extremal" volume ratio, then it has a projection of proportional dimension which is close to the cube. We compare type 2 and infratype 2 constant of a Banach space. This follows from a comparison lemma for Rademacher and Gaussian averages. We also establish a sharp estimate on the shattering dimension of the convex hull of a class of functions in terms of the shattering dimension of the class itself.

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S. Mendelson, R. Vershynin. 2003-06-22. Remarks on the geometry of coordinate projections in R^n. https://arxiv.org/abs/math/0306314

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