Moments of unconditional logarithmically concave vectors
Rafa{\l} Lata{\l}a
TL;DR
This paper establishes bounds for moments of linear combinations of unconditional log-concave vectors and compares these moments to those of Gaussian variables, enhancing understanding of their probabilistic behavior.
Contribution
It provides new two-sided bounds for moments of unconditional log-concave vectors and analyzes their approximation by Gaussian moments, a novel contribution in this area.
Findings
Derived two-sided bounds for moments of linear combinations
Compared moments of log-concave vectors with Gaussian moments
Enhanced understanding of probabilistic properties of such vectors
Abstract
We derive two-sided bounds for moments of linear combinations of coordinates od unconditional log-concave vectors. We also investigate how well moments of such combinations may be approximated by moments of Gaussian random variables.
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