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

Factor impacto JCR: 0.87 (2016)

Categ. JCR: MATHEMATICS rank: 81 / 310 = 0.261 (2016) - Q2 - T1

Factor impacto SCIMAGO: 1.647 - Geometry and Topology (Q1)

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): Área Análisis Matemático (Dpto. Matemáticas)