Order statistics and concentration of l_r norms for log-concave vectors

TL;DR

This paper derives upper bounds for the tail probabilities of order statistics of isotropic log-concave vectors and uses these results to analyze the concentration behavior of their l_r norms.

Contribution

It provides new tail bounds for order statistics and applies them to establish concentration inequalities for l_r norms of log-concave vectors.

Findings

Upper bounds for tails of order statistics

Concentration inequalities for l_r norms

Enhanced understanding of log-concave vector behavior

Abstract

We establish upper bounds for tails of order statistics of isotropic log-concave vectors and apply them to derive a concentration of l_r norms of such vectors.