Vol. 2, No. 2, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN (electronic): 2690-1005
ISSN (print): 2690-0998
Author Index
To Appear
Other MSP Journals
Spectral radius of random matrices with independent entries

Johannes Alt, László Erdős and Torben Krüger

Vol. 2 (2021), No. 2, 221–280

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 (Ann. Appl. Probab. 28:1 (2018), 148–203) at the spectral edge.

spectral radius, inhomogeneous circular law, cusp local law
Mathematical Subject Classification 2010
Primary: 15B52, 60B20
Received: 6 February 2020
Revised: 15 October 2020
Accepted: 25 December 2020
Published: 22 May 2021
Johannes Alt
Section de mathématiques
Université de Genève
László Erdős
Institute of Science and Technology Austria
Torben Krüger
Department of Mathematical Sciences
University of Copenhagen