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)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes.
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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)
You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. Exportado de SIDERAL (2020-02-21-13:17:50)
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Record created 2017-01-09, last modified 2020-02-21