Open Access
2024 Central limit theorem for the complex eigenvalues of Gaussian random matrices
Advay Goel, Patrick Lopatto, Xiaoyu Xie
Author Affiliations +
Electron. Commun. Probab. 29: 1-13 (2024). DOI: 10.1214/24-ECP585


We establish a central limit theorem for the eigenvalue counting function of a matrix of real Gaussian random variables.

Funding Statement

P. L. was supported by the NSF postdoctoral fellowship DMS-2202891. X. X. was supported by NSF grant DMS-1954351.


The authors thank P. Bourgade for suggesting the problem, C. D. Sinclair for helpful comments on the references [3, 32], and P. J. Forrester for comments on a preliminary draft. They are grateful to the referees for several useful suggestions.


Download Citation

Advay Goel. Patrick Lopatto. Xiaoyu Xie. "Central limit theorem for the complex eigenvalues of Gaussian random matrices." Electron. Commun. Probab. 29 1 - 13, 2024.


Received: 23 October 2023; Accepted: 5 March 2024; Published: 2024
First available in Project Euclid: 25 March 2024

Digital Object Identifier: 10.1214/24-ECP585

Primary: 60B20

Keywords: Ginibre ensemble , Random matrix

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