On the Isotropic Constant of Random Polytopes
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Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
On the Isotropic Constant of Random PolytopesDate
2015-01Publisher
Springer Verlag; Mathematica Josephina, Inc.Bibliographic citation
ALONSO-GUTIÉRREZ, David; LITVAK, Alexander E.; TOMCZAK-JAEGERMANN, Nicole. On the isotropic constant of random polytopes. The Journal of Geometric Analysis, 2016, vol. 26, no 1, p. 645-662.Type
info:eu-repo/semantics/articlePublisher version
http://link.springer.com/article/10.1007/s12220-015-9567-9#enumerationVersion
info:eu-repo/semantics/sumittedVersionSubject
Abstract
Let X1,…,XN be independent random vectors uniformly distributed on an isotropic convex body K ⊂ Rn, and let KN be the symmetric convex hull of Xi’s. We show that with high probability LKN ≤ C√log(2N/n), where C is an ... [+]
Let X1,…,XN be independent random vectors uniformly distributed on an isotropic convex body K ⊂ Rn, and let KN be the symmetric convex hull of Xi’s. We show that with high probability LKN ≤ C√log(2N/n), where C is an absolute constant. This result closes the gap in known estimates in the range Cn ≤ N ≤ n1+δ. Furthermore, we extend our estimates to the symmetric convex hulls of vectors y1 X1,…,yN XN, where y = (y1,…,yN) is a vector in RN. Finally, we discuss the case of a random vector y. [-]
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The Journal of Geometric Analysis, 2016, vol. 26, no 1Rights
© Mathematica Josephina, Inc. 2015
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- MAT_Articles [761]