On the singular values of random matrices

Mendelson, Shahar, and Paouris, Grigoris. "On the singular values of random matrices." Journal of the European Mathematical Society 016.4 (2014): 823-834. <http://eudml.org/doc/277248>.

@article{Mendelson2014,
abstract = {We present an approach that allows one to bound the largest and smallest singular values of an $N \times n$ random matrix with iid rows, distributed according to a measure on $\mathbb \{R\}^n$ that is supported in a relatively small ball and linear functionals are uniformly bounded in $L_p$ for some $p>8$, in a quantitative (non-asymptotic) fashion. Among the outcomes of this approach are optimal estimates of $1 \pm c\sqrt\{n/N\}$ not only in the case of the above mentioned measure, but also when the measure is log-concave or when it a product measure of iid random variables with “heavy tails”.},
author = {Mendelson, Shahar, Paouris, Grigoris},
journal = {Journal of the European Mathematical Society},
keywords = {singular values; random matrices; heavy tails; singular values; random matrices; heavy tails},
language = {eng},
number = {4},
pages = {823-834},
publisher = {European Mathematical Society Publishing House},
title = {On the singular values of random matrices},
url = {http://eudml.org/doc/277248},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Mendelson, Shahar
AU - Paouris, Grigoris
TI - On the singular values of random matrices
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 4
SP - 823
EP - 834
AB - We present an approach that allows one to bound the largest and smallest singular values of an $N \times n$ random matrix with iid rows, distributed according to a measure on $\mathbb {R}^n$ that is supported in a relatively small ball and linear functionals are uniformly bounded in $L_p$ for some $p>8$, in a quantitative (non-asymptotic) fashion. Among the outcomes of this approach are optimal estimates of $1 \pm c\sqrt{n/N}$ not only in the case of the above mentioned measure, but also when the measure is log-concave or when it a product measure of iid random variables with “heavy tails”.
LA - eng
KW - singular values; random matrices; heavy tails; singular values; random matrices; heavy tails
UR - http://eudml.org/doc/277248
ER -