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On the Isotropic Constant of Random Polytopes
| dc.contributor.author | Alonso Gutiérrez, David | |
| dc.contributor.author | Litvak, Alexander E. | |
| dc.contributor.author | Tomczak-Jaegermann, Nicole | |
| dc.date.accessioned | 2017-02-07T13:31:53Z | |
| dc.date.available | 2017-02-07T13:31:53Z | |
| dc.date.issued | 2015-01 | |
| dc.identifier.citation | 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. | ca_CA |
| dc.identifier.uri | http://hdl.handle.net/10234/165894 | |
| dc.description.abstract | 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. | ca_CA |
| dc.description.sponsorShip | Part of this work was done while the first named author was a postdoctoral fellow at the Department of Mathematical and Statistical Sciences at University of Alberta, and continued while he was a “Juan de la Cierva” postdoctoral researcher at the Mathematics Department in Universidad de Murcia. He would like to thank both departments for providing support, good environment and working conditions. We would also like to thank the anonymous referee for careful reading of the manuscript and for informing us that Theorem 1.1 has subsequently been proved also in [17] using essentially the same approach. Finally we are very thankful to Rafał Latała for showing us the argument in Lemma 5.2. David Alonso-Gutiérrez is Partially supported by MICINN project MTM2010-16679, MICINN-FEDER project MTM2009-10418, “Programa de Ayudas a Grupos de Excelencia de la Región de Murcia”, Fundación Séneca, 04540/GERM/06 and Institut Universitari de Matemàtiques i Aplicacions de Castelló Alexander E. Litvak Research partially supported by the E.W.R. Steacie Memorial Fellowship Nicole Tomczak-Jaegermann holds the Canada Research Chair in Geometric Analysis. | ca_CA |
| dc.format.extent | 17 p. | ca_CA |
| dc.format.mimetype | application/pdf | ca_CA |
| dc.language.iso | eng | ca_CA |
| dc.publisher | Springer Verlag | ca_CA |
| dc.publisher | Mathematica Josephina, Inc. | ca_CA |
| dc.relation.isPartOf | The Journal of Geometric Analysis, 2016, vol. 26, no 1 | ca_CA |
| dc.rights | © Mathematica Josephina, Inc. 2015 | ca_CA |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | * |
| dc.subject | convex bodies | ca_CA |
| dc.subject | isotropic measures | ca_CA |
| dc.subject | isotropic constant | ca_CA |
| dc.subject | random polytopes | ca_CA |
| dc.title | On the Isotropic Constant of Random Polytopes | ca_CA |
| dc.type | info:eu-repo/semantics/article | ca_CA |
| dc.identifier.doi | http://dx.doi.org/10.1007/s12220-015-9567-9 | |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
| dc.relation.publisherVersion | http://link.springer.com/article/10.1007/s12220-015-9567-9#enumeration | ca_CA |
| dc.type.version | info:eu-repo/semantics/sumittedVersion |
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