L_p moments of random vectors via majorizing measures
| dc.creator | Guedon, Olivier | |
| dc.creator | Rudelson, Mark | |
| dc.date | 2005-07-01 | |
| dc.date | 2006-04-04 | |
| dc.date.accessioned | 2026-07-07T06:42:34Z | |
| dc.date.available | 2026-07-07T06:42:34Z | |
| dc.description | For a random vector X in R^n, we obtain bounds on the size of a sample, for which the empirical p-th moments of linear functionals are close to the exact ones uniformly on an n-dimensional convex body K. We prove an estimate for a general random vector and apply it to several problems arising in geometric functional analysis. In particular, we find a short Lewis type decomposition for any finite dimensional subspace of L_p. We also prove that for an isotropic log-concave random vector, we only need about n^{p/2} \log n sample points so that the empirical p-th moments of the linear functionals are almost isometrically the same as the exact ones. We obtain a concentration estimate for the empirical moments. The main ingredient of the proof is the construction of an appropriate majorizing measure to bound a certain Gaussian process. | |
| dc.description | 32 pages, to appear in Advances in Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0507023 | |
| dc.identifier | http://arxiv.org/abs/math/0507023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102086 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B09, 52A21 | |
| dc.title | L_p moments of random vectors via majorizing measures | |
| dc.type | text |