The spectral norm of Gaussian matrices with correlated entries

Afonso S. Bandeira; March T. Boedihardjo

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arXiv · 2104.02662

The spectral norm of Gaussian matrices with correlated entries

Afonso S. Bandeira·March T. Boedihardjo

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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.

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Afonso S. Bandeira, March T. Boedihardjo. 2021-04-06. The spectral norm of Gaussian matrices with correlated entries. https://arxiv.org/abs/2104.02662

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