The variance conjecture on hyperplane projections of the $\ell_p^n$ balls
| Autor: | Jesús Bastero, David Alonso-Gutiérrez |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Unit sphere
Conjecture Multivariate random variable General Mathematics 010102 general mathematics 0102 computer and information sciences Variance (accounting) 01 natural sciences Combinatorics Hyperplane Dimension (vector space) 010201 computation theory & mathematics Symmetrization Convex body 0101 mathematics Mathematics |
| Zdroj: | Revista Matemática Iberoamericana. 34:879-904 |
| ISSN: | 0213-2230 |
| DOI: | 10.4171/rmi/1007 |
| Popis: | We show that for any 1≤p≤∞, the family of random vectors uniformly distributed on hyperplane projections of the unit ball of lnp verify the variance conjecture Var|X|2≤Cmaxξ∈Sn−1E⟨X,ξ⟩2E|X|2, 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 lnp-ball verify the variance conjecture. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|