On the isotropy constant of random polytopes

Alonso Gutiérrez, David; Tomczak-Jaegermann, Nicole; Litvak, Alexander

doi:10.1007/s12220-015-9567-9

On the isotropy constant of random polytopes

Alonso Gutiérrez, David (Universidad de Zaragoza) ; Litvak, Alexander ; Tomczak-Jaegermann, Nicole

Resumen: Let X 1 , . . . , X N 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+d. Furthermore, we extend our estimates to the symmetric convex hulls of vectors y1 X1, . . . , yN X N , where y = (y1, . . . , yN ) is a vector in RN . Finally, we discuss the case of a random vector y.
Idioma: Inglés
DOI: 10.1007/s12220-015-9567-9
Año: 2016
Publicado en: JOURNAL OF GEOMETRIC ANALYSIS 26 (2016), 645-662
ISSN: 1050-6926
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2009-10418
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2010-16679
Tipo y forma: Article (PostPrint)
Área (Departamento): Análisis Matemático (Departamento de Matemáticas)

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On the isotropy constant of random polytopes