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Small ball probability and Dvoretzky’s Theorem

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Abstract

Large deviation estimates are by now a standard tool in Asymptotic Convex Geometry, contrary to small deviation results. In this note we present a novel application of a small deviations inequality to a problem that is related to the diameters of random sections of high dimensional convex bodies. Our results imply an unexpected distinction between the lower and upper inclusions in Dvoretzky’s Theorem.

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Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, Princeton, NJ, 08540, USA

    B. Klartag

  2. Department of Mathematics, University of California, One Shields Ave, Davis, CA, 95616, USA

    R. Vershynin

Authors
  1. B. Klartag
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  2. R. Vershynin
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Supported by NSF grant DMS-0111298 and the Bell Companies Fellowship.

Supported by NSF grant 0401032 and the Sloan Research Fellowship.

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Klartag, B., Vershynin, R. Small ball probability and Dvoretzky’s Theorem. Isr. J. Math. 157, 193–207 (2007). https://doi.org/10.1007/s11856-006-0007-1

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  • DOI: https://doi.org/10.1007/s11856-006-0007-1

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