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The variance conjecture on hyperplane projections of the lpn balls.
- Source :
- Revista Mathematica Iberoamericana; 2018, Vol. 34 Issue 2, p879-904, 26p
- Publication Year :
- 2018
-
Abstract
- We show that for any 1 ≤ p ≤ ∞, the family of random vectors uniformly distributed on hyperplane projections of the unit ball of l<subscript>p</subscript><superscript>n</superscript> verify the variance conjecture Var ∣X∣<superscript>2</superscript> ≤ C max ξ∈Sn<superscript>-1</superscript> E<X, ξ><superscript>2</superscript> E∣X∣2<superscript>,</superscript> where C depends on p but not on the dimension n or the hyperplane. We will also show a general result relating the variance conjecture for a random vector uniformly distributed on an isotropic convex body and the variance conjecture for a random vector uniformly distributed on any Steiner symmetrization of it. As a consequence we will have that the class of random vectors uniformly distributed on any Steiner symmetrization of an l<subscript>p</subscript><superscript>n</superscript> -ball verify the variance conjecture. [ABSTRACT FROM AUTHOR]
- Subjects :
- STEINER systems
CONVEX geometry
HYPERPLANES
LEBESGUE measure
MEASURE theory
Subjects
Details
- Language :
- English
- ISSN :
- 02132230
- Volume :
- 34
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Revista Mathematica Iberoamericana
- Publication Type :
- Academic Journal
- Accession number :
- 129968503
- Full Text :
- https://doi.org/10.4171/rmi/1007