On the singular values of random matrices Academic Article

abstract

• 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.

authors

• Paouris, Grigoris

published proceedings

• JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY

author list (cited authors)

• Mendelson, S., & Paouris, G.

citation count

• 25

complete list of authors

• Mendelson, Shahar||Paouris, Grigoris

publication date

• January 2014

publisher

• European Mathematical Society - EMS - Publishing House GmbH  Publisher

published in

• Journal of the European Mathematical Society (Print)  Journal

keywords

• Heavy Tails
• Random Matrices
• Singular Values

Digital Object Identifier (DOI)

• 10.4171/JEMS/448

start page

• 823

end page

• 834

volume

• 16

issue

• 4

URL

• http://dx.doi.org/10.4171/jems/448