On the Isotropic Constant of Random Polytopes
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Otros documentos de la autoría: Alonso Gutiérrez, David; Litvak, Alexander E.; Tomczak-Jaegermann, Nicole
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Título
On the Isotropic Constant of Random PolytopesFecha de publicación
2015-01Editor
Springer Verlag; Mathematica Josephina, Inc.Cita bibliográfica
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.Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
http://link.springer.com/article/10.1007/s12220-015-9567-9#enumerationVersión
info:eu-repo/semantics/sumittedVersionPalabras clave / Materias
Resumen
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 1Derechos de acceso
© Mathematica Josephina, Inc. 2015
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