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We establish two-sided bounds for expectations of order statistics ($k$-thmaxima) of moduli of coordinates of centered log-concave random vectors withuncorrelated coordinates. Our bounds are exact up to multiplicative universalconstants 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 ofsums of $k$ largest moduli of coordinates for some classes of random vectors.

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