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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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