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This paper investigates an upper bound of the operator norm for sub-Gaussiantailed random matrices. A lot of attention has been put on uniformly boundedsub-Gaussian tailed random matrices with independent coefficients. However,little has been done for sub-Gaussian tailed random matrices whose matrixcoefficients variance are not equal or for matrix for which coefficients arenot independent. This is precisely the subject of this paper. After provingthat random matrices with uniform sub-Gaussian tailed independent coefficientssatisfy the Tracy Widom bound, that is, their matrix operator norm remainsbounded by $O(\sqrt n )$ with overwhelming probability, we prove that a lessstringent condition is that the matrix rows are independent and uniformlysub-Gaussian. This does not impose in particular that all matrix coefficientsare independent, but only their rows, which is a weaker condition.

Operator norm upper bound for sub-Gaussian tailed random matrices