On the spectral edge of non-Hermitian random matrices
Campbell AJ, Cipolloni G, Erdös L, Ji HC. 2025. On the spectral edge of non-Hermitian random matrices. The Annals of Probability. 53(6), 2256–2308.
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Abstract
For general non-Hermitian large random matrices X and deterministic deformation matrices A, we prove that the local eigenvalue statistics of A+X close to the typical edge points of its spectrum are universal. Furthermore, we show that, under natural assumptions, on A the spectrum of A+X does not have outliers at a distance larger than the natural fluctuation scale of the eigenvalues. As a consequence, the number of eigenvalues in each component of Spec(A+X) is deterministic.
Publishing Year
Date Published
2025-11-01
Journal Title
The Annals of Probability
Publisher
Institute of Mathematical Statistics
Acknowledgement
The authors would like to thank the anonymous referee for providing helpful comments and suggestions. We also thank Joscha Henheik and Volodymyr Riabov for pointing out a gap in an earlier version of the proof of equation (3.18). The first, third, and fourth authors are supported by ERC Advanced Grant “RMTBeyond” No. 101020331.
Volume
53
Issue
6
Page
2256-2308
ISSN
eISSN
IST-REx-ID
Cite this
Campbell AJ, Cipolloni G, Erdös L, Ji HC. On the spectral edge of non-Hermitian random matrices. The Annals of Probability. 2025;53(6):2256-2308. doi:10.1214/25-aop1761
Campbell, A. J., Cipolloni, G., Erdös, L., & Ji, H. C. (2025). On the spectral edge of non-Hermitian random matrices. The Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/25-aop1761
Campbell, Andrew J, Giorgio Cipolloni, László Erdös, and Hong Chang Ji. “On the Spectral Edge of Non-Hermitian Random Matrices.” The Annals of Probability. Institute of Mathematical Statistics, 2025. https://doi.org/10.1214/25-aop1761.
A. J. Campbell, G. Cipolloni, L. Erdös, and H. C. Ji, “On the spectral edge of non-Hermitian random matrices,” The Annals of Probability, vol. 53, no. 6. Institute of Mathematical Statistics, pp. 2256–2308, 2025.
Campbell AJ, Cipolloni G, Erdös L, Ji HC. 2025. On the spectral edge of non-Hermitian random matrices. The Annals of Probability. 53(6), 2256–2308.
Campbell, Andrew J., et al. “On the Spectral Edge of Non-Hermitian Random Matrices.” The Annals of Probability, vol. 53, no. 6, Institute of Mathematical Statistics, 2025, pp. 2256–308, doi:10.1214/25-aop1761.
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