The spectral norm of Gaussian matrices with correlated entries

Afonso S. Bandeira; March T. Boedihardjo

The spectral norm of Gaussian matrices with correlated entries

Probability 2021-08-24 v3

Authors: Afonso S. Bandeira , March T. Boedihardjo

Abstract

We give a non-asymptotic bound on the spectral norm of a $d\times d$ matrix $X$ with centered jointly Gaussian entries in terms of the covariance matrix of the entries. In some cases, this estimate is sharp and removes the $\sqrt{\log d}$ factor in the noncommutative Khintchine inequality.

Keywords

spectral norm gaussian matrices correlated entries covariance matrix non-asymptotic bound noncommutative khintchine inequality

Cite

@article{arxiv.2104.02662,
  title  = {The spectral norm of Gaussian matrices with correlated entries},
  author = {Afonso S. Bandeira and March T. Boedihardjo},
  journal= {arXiv preprint arXiv:2104.02662},
  year   = {2021}
}

Comments

This paper is superseded by arXiv:2108.06312

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