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arXiv · 1209.4270

The variance conjecture on some polytopes

David Alonso-Gutiérrez·Jesús Bastero
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Abstract

We show that any random vector uniformly distributed on any hyperplane projection of $B_1^n$ or $B_\infty^n$ verifies the variance conjecture $$\text{Var}|X|^2\leq C\sup_{ξ\in S^{n-1}}\E ^2\E|X|^2.$$ Furthermore, a random vector uniformly distributed on a hyperplane projection of $B_\infty^n$ verifies a negative square correlation property and consequently any of its linear images verifies the variance conjecture.

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David Alonso-Gutiérrez, Jesús Bastero. 2012-09-19. The variance conjecture on some polytopes. https://arxiv.org/abs/1209.4270

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