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Spectral radius of random
matrices with independent entries
Johannes Alt, László Erdős and Torben Krüger |
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Vol. 2 (2021), No. 2, 221–280
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Abstract |
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We consider random matrices with independent and centered entries and a general variance profile. We show that the spectral radius of converges with very high probability to the square root of the spectral radius of the variance matrix of when 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 (Ann. Appl. Probab. 28:1 (2018), 148–203) at the spectral edge. |
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Keywords
spectral radius, inhomogeneous circular law, cusp local law
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Mathematical Subject Classification 2010
Primary: 15B52, 60B20
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Milestones
Received: 6 February 2020
Revised: 15 October 2020
Accepted: 25 December 2020
Published: 22 May 2021
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Authors |
| Johannes Alt | |
| Section de mathématiques Université de Genève Geneve Switzerland |
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| László Erdős | |
| Institute of Science and Technology
Austria Klosterneuburg Austria |
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| Torben Krüger | |
| Department of Mathematical
Sciences University of Copenhagen Copenhagen Denmark |
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