000058427 001__ 58427 000058427 005__ 20200221144226.0 000058427 0247_ $$2doi$$a10.1007/s12220-015-9567-9 000058427 0248_ $$2sideral$$a97164 000058427 037__ $$aART-2016-97164 000058427 041__ $$aeng 000058427 100__ $$0(orcid)0000-0003-1256-3671$$aAlonso Gutiérrez, David$$uUniversidad de Zaragoza 000058427 245__ $$aOn the isotropy constant of random polytopes 000058427 260__ $$c2016 000058427 5060_ $$aAccess copy available to the general public$$fUnrestricted 000058427 5203_ $$aLet 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. 000058427 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2009-10418$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2010-16679 000058427 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc$$uhttp://creativecommons.org/licenses/by-nc/3.0/es/ 000058427 590__ $$a0.87$$b2016 000058427 591__ $$aMATHEMATICS$$b81 / 310 = 0.261$$c2016$$dQ2$$eT1 000058427 592__ $$a1.647$$b2016 000058427 593__ $$aGeometry and Topology$$c2016$$dQ1 000058427 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000058427 700__ $$aLitvak, Alexander 000058427 700__ $$aTomczak-Jaegermann, Nicole 000058427 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000058427 773__ $$g26 (2016), 645-662$$pJ. geom. anal.$$tJOURNAL OF GEOMETRIC ANALYSIS$$x1050-6926 000058427 8564_ $$s402693$$uhttps://zaguan.unizar.es/record/58427/files/texto_completo.pdf$$yPostprint 000058427 8564_ $$s51096$$uhttps://zaguan.unizar.es/record/58427/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000058427 909CO $$ooai:zaguan.unizar.es:58427$$particulos$$pdriver 000058427 951__ $$a2020-02-21-13:17:50 000058427 980__ $$aARTICLE