The variance conjecture on some polytopes

2012/09/19 by Alonso-Gutiérrez, David, Bastero, Jesús · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1209.4270

Abstract

We show that any random vector uniformly distributed on any hyperplane projection of B₁ⁿ or B_∞ⁿ verifies the variance conjecture Var|X|²≤ Csup_{ξ∈ S^n-1}\E²\E|X|². Furthermore, a random vector uniformly distributed on a hyperplane projection of B_∞ⁿ verifies a negative square correlation property and consequently any of its linear images verifies the variance conjecture.

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• Optimal MM^* bounds for convex bodies

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