Geodesic
On the singular values of random matrices
Journal of the European Mathematical Society, Tome 16 (2014) no. 4, pp. 823-834

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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 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 a product measure of iid random variables with "heavy tails".
DOI : 10.4171/jems/448
Classification : 60-XX, 00-XX
Keywords: Singular values, random matrices, heavy tails 
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Shahar Mendelson; Grigoris Paouris. On the singular values of random matrices. Journal of the European Mathematical Society, Tome 16 (2014) no. 4, pp. 823-834. doi: 10.4171/jems/448

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