On the singular values of random matrices Academic Article uri icon


  • We present an approach that allows one to bound the largest and smallest singular values of an Nn random matrix with iid rows, distributed according to a measure on Rn that is supported in a relatively small ball and for which linear functionals are uniformly bounded in Lp for some p > 8, in a quantitative (non-asymptotic) fashion. Among the outcomes of this approach are optimal estimates of 1 cn=N not only in the case of the above mentioned measure, but also when the measure is log-concave or when it is a product measure of iid random variables with "heavy tails". European Mathematical Society 2014.

published proceedings


author list (cited authors)

  • Mendelson, S., & Paouris, G.

citation count

  • 25

complete list of authors

  • Mendelson, Shahar||Paouris, Grigoris

publication date

  • January 2014