article
Small ball probability and Dvoretzky’s Theorem
Bo’az Klartaga b, Roman Vershyninc d
- aSchool of Mathematics, Institute for Advanced Study, Princeton, NJ, 08540, USA
- bSchool of Mathematics , Institute for Advanced Study , Princeton , USA
- cDepartment of Mathematics, University of California, One Shields Ave, Davis, CA, 95616, USA
- d[Department of Mathematics, University of California, Davis, USA]
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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.