Sharp nonasymptotic bounds on the norm of random matrices with independent entries

@article{Bandeira2014SharpNB,
  title={Sharp nonasymptotic bounds on the norm of random matrices with independent entries},
  author={A. Bandeira and R. Handel},
  journal={arXiv: Probability},
  year={2014}
}
We obtain nonasymptotic bounds on the spectral norm of random matrices with independent entries that improve significantly on earlier results. If $X$ is the $n\times n$ symmetric matrix with $X_{ij}\sim N(0,b_{ij}^2)$, we show that \[\mathbf{E}\Vert X\Vert \lesssim\max_i\sqrt{\sum_jb_{ij}^2}+\max _{ij}\vert b_{ij}\vert \sqrt{\log n}.\] This bound is optimal in the sense that a matching lower bound holds under mild assumptions, and the constants are sufficiently sharp that we can often capture… Expand
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