TY - JOUR

T1 - Small ball probability and Dvoretzky's Theorem

AU - Klartag, B.

AU - Vershynin, R.

N1 - Funding Information:
Supported by NSF grant DMS-0111298 and the Bell Companies Fellowship. Supported by NSF grant 0401032 and the Sloan Research Fellowship. Received September 30, 2004

PY - 2007/1

Y1 - 2007/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=41449097539&partnerID=8YFLogxK

U2 - 10.1007/s11856-006-0007-1

DO - 10.1007/s11856-006-0007-1

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AN - SCOPUS:41449097539

SN - 0021-2172

VL - 157

SP - 193

EP - 207

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -