# On the singular values of random matrices

Shahar Mendelson; Grigoris Paouris

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 4, page 823-834
- ISSN: 1435-9855

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topMendelson, 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 -

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