English

The variance conjecture on some polytopes

Functional Analysis 2012-09-20 v1

Abstract

We show that any random vector uniformly distributed on any hyperplane projection of B1nB_1^n or BnB_\infty^n verifies the variance conjecture VarX2CsupξSn1\E<X,ξ>2\EX2.\text{Var}|X|^2\leq C\sup_{\xi\in S^{n-1}}\E<X,\xi>^2\E|X|^2. Furthermore, a random vector uniformly distributed on a hyperplane projection of BnB_\infty^n verifies a negative square correlation property and consequently any of its linear images verifies the variance conjecture.

Keywords

Cite

@article{arxiv.1209.4270,
  title  = {The variance conjecture on some polytopes},
  author = {David Alonso-Gutiérrez and Jesús Bastero},
  journal= {arXiv preprint arXiv:1209.4270},
  year   = {2012}
}
R2 v1 2026-06-21T22:07:56.313Z