On the singular values of random matrices

Shahar Mendelson; Grigoris Paouris

doi:10.4171/JEMS/448

On the singular values of random matrices

Shahar Mendelson, Grigoris Paouris

Research output: Contribution to journal › Article › peer-review

34 Citations (Scopus)

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 L_p 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".

Original language	English
Pages (from-to)	823-834
Number of pages	12
Journal	Journal of the European Mathematical Society
Volume	16
Issue number	4
DOIs	https://doi.org/10.4171/JEMS/448
Publication status	Published - 2014
Externally published	Yes

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On the singular values of random matrices

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