Uniform Estimates for Averages of Order Statistics of Matrices

TL;DR

This paper establishes uniform bounds for the expected averages of order statistics of matrices based on their largest entries, with applications to probabilistic estimates of b5 norms through real interpolation.

Contribution

It introduces new uniform estimates linking order statistic averages to matrix entries and applies these results to b5 norm estimates via real interpolation.

Findings

Uniform estimates for order statistic averages in matrices.

Probabilistic bounds for b5 norms derived from matrix entries.

Application of real interpolation techniques.

Abstract

We prove uniform estimates for the expected value of averages of order statistics of matrices in terms of their largest entries. As an application, we obtain similar probabilistic estimates for $\ell_p$ norms via real interpolation.