TY - JOUR
T1 - Power-law estimates for the central limit theorem for convex sets
AU - Klartag, B.
N1 - Funding Information:
1 The author is a Clay Research Fellow and is also supported by NSF grant #DMS-0456590.
PY - 2007/4/1
Y1 - 2007/4/1
N2 - We investigate the rate of convergence in the central limit theorem for convex sets established in [B. Klartag, A central limit theorem for convex sets, Invent. Math., in press. [8]]. We obtain bounds with a power-law dependence on the dimension. These bounds are asymptotically better than the logarithmic estimates which follow from the original proof of the central limit theorem for convex sets.
AB - We investigate the rate of convergence in the central limit theorem for convex sets established in [B. Klartag, A central limit theorem for convex sets, Invent. Math., in press. [8]]. We obtain bounds with a power-law dependence on the dimension. These bounds are asymptotically better than the logarithmic estimates which follow from the original proof of the central limit theorem for convex sets.
KW - Central limit theorem
KW - Convex bodies
KW - Marginal distribution
UR - http://www.scopus.com/inward/record.url?scp=33847356533&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2006.12.005
DO - 10.1016/j.jfa.2006.12.005
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AN - SCOPUS:33847356533
SN - 0022-1236
VL - 245
SP - 284
EP - 310
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -