The square negative correlation property for generalized Orlicz balls

dc.creatorWojtaszczyk, Jakub Onufry
dc.date2008-03-04
dc.date.accessioned2026-07-07T09:24:34Z
dc.date.available2026-07-07T09:24:34Z
dc.descriptionAntilla, 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.description10 pages
dc.identifierhttps://arxiv.org/abs/0803.0433
dc.identifierhttp://arxiv.org/abs/0803.0433
dc.identifierGeometric Aspects of Functional Analysis, Israel Seminar, 2004-2005, pp. 305-313
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156139
dc.subjectProbability
dc.subjectFunctional Analysis
dc.subject52A20, 60D05
dc.titleThe square negative correlation property for generalized Orlicz balls
dc.typetext

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