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

Rafał Latała; Marta Strzelecka

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

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arXiv · 1901.01587

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

Rafał Latała·Marta Strzelecka

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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 $k \leq n-cn^{5/6}$. We also derive two-sided estimates for expectations of sums of $k$ largest moduli of coordinates for some classes of random vectors.

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Rafał Latała, Marta Strzelecka. 2019-01-06. Two-sided estimates for order statistics of log-concave random vectors. https://doi.org/10.1007/978-3-030-46762-3_3

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