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 -