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arXiv · 1907.13631

Spectral radius of random matrices with independent entries

Johannes Alt·Laszlo Erdos·Torben Krüger
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Abstract

We consider random $n\times n$ matrices $X$ with independent and centered entries and a general variance profile. We show that the spectral radius of $X$ converges with very high probability to the square root of the spectral radius of the variance matrix of $X$ when $n$ tends to infinity. We also establish the optimal rate of convergence, that is a new result even for general i.i.d. matrices beyond the explicitly solvable Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular law [arXiv:1612.07776] at the spectral edge.

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BibTeXRIS

Johannes Alt, Laszlo Erdos, Torben Krüger. 2019-07-31. Spectral radius of random matrices with independent entries. https://doi.org/10.2140/pmp.2021.2.221

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