Two-sided estimates for order statistics of log-concave random vectors

Rafał Latała; Marta Strzelecka

doi:10.1007/978-3-030-46762-3_3

paper

Two-sided estimates for order statistics of log-concave random vectors

arXiv:1901.01587 · doi:10.1007/978-3-030-46762-3_3

Abstract

We establish two-sided bounds for expectations of order statistics ( $k$ -th maxima) of moduli of coordinates of centered log-concave random vectors with uncorrelated coordinates. Our bounds are exact up to multiplicative universal constants in the unconditional case for all $k$ and in the isotropic case for $k \leq n - c n^{5/6}$ . We also derive two-sided estimates for expectations of sums of $k$ largest moduli of coordinates for some classes of random vectors.

25 pages