On the singular values of random matrices Academic Article uri icon

abstract

  • We present an approach that allows one to bound the largest and smallest singular values of an N×n 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 ± c√n=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.

author list (cited authors)

  • Mendelson, S., & Paouris, G.

publication date

  • January 1, 2014 11:11 AM