# Spectral radius of random matrices with independent entries

Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280.

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https://doi.org/10.48550/arXiv.1907.13631
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*Journal Article*|

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*English*

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Abstract

We consider random n×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.

Publishing Year

Date Published

2021-05-21

Journal Title

Probability and Mathematical Physics

Acknowledgement

Partially supported by ERC Starting Grant RandMat No. 715539 and the SwissMap grant of Swiss National Science Foundation. Partially supported by ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center for Mathematics in Bonn.

Volume

2

Issue

2

Page

221-280

ISSN

eISSN

IST-REx-ID

### Cite this

Alt J, Erdös L, Krüger TH. Spectral radius of random matrices with independent entries.

*Probability and Mathematical Physics*. 2021;2(2):221-280. doi:10.2140/pmp.2021.2.221Alt, J., Erdös, L., & Krüger, T. H. (2021). Spectral radius of random matrices with independent entries.

*Probability and Mathematical Physics*. Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2021.2.221Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random Matrices with Independent Entries.”

*Probability and Mathematical Physics*. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/pmp.2021.2.221.J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with independent entries,”

*Probability and Mathematical Physics*, vol. 2, no. 2. Mathematical Sciences Publishers, pp. 221–280, 2021.Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent Entries.”

*Probability and Mathematical Physics*, vol. 2, no. 2, Mathematical Sciences Publishers, 2021, pp. 221–80, doi:10.2140/pmp.2021.2.221.**All files available under the following license(s):**

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arXiv 1907.13631