The square negative correlation property for generalized Orlicz balls
| dc.creator | Wojtaszczyk, Jakub Onufry | |
| dc.date | 2008-03-04 | |
| dc.date.accessioned | 2026-07-07T09:24:34Z | |
| dc.date.available | 2026-07-07T09:24:34Z | |
| dc.description | Antilla, Ball and Perissinaki proved that the squares of coordinate functions in $\ell_p^n$ are negatively correlated. This paper extends their results to balls in generalized Orlicz norms on R^n. From this, the concentration of the Euclidean norm and a form of the Central Limit Theorem for the generalized Orlicz balls is deduced. Also, a counterexample for the square negative correlation hypothesis for 1-symmetric bodies is given. Currently the CLT is known in full generality for convex bodies (see the paper "Power-law estimates for the central limit theorem for convex sets" by B. Klartag), while for generalized Orlicz balls a much more general result is true (see "The negative association property for the absolute values of random variables equidistributed on a generalized Orlicz ball" by M. Pilipczuk and J. O. Wojtaszczyk). While, however, both aforementioned papers are rather long, complicated and technical, this paper gives a simple and elementary proof of, eg., the Euclidean concentration for generalized Orlicz balls. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0803.0433 | |
| dc.identifier | http://arxiv.org/abs/0803.0433 | |
| dc.identifier | Geometric Aspects of Functional Analysis, Israel Seminar, 2004-2005, pp. 305-313 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156139 | |
| dc.subject | Probability | |
| dc.subject | Functional Analysis | |
| dc.subject | 52A20, 60D05 | |
| dc.title | The square negative correlation property for generalized Orlicz balls | |
| dc.type | text |