Order Statistics of Log-Concave Vectors

Abstract: I will discuss 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 = n-cn^{5/6}. We also present two-sided estimates for expectations of sums of k largest moduli of coordinates for some classes of random vectors. Joint work with Marta Strzelecka.

analysis of PDEsmetric geometryprobability

Audience: researchers in the topic

Online asymptotic geometric analysis seminar

Series comments: The link: technion.zoom.us/j/99202255210

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