Abstract
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.
Acknowledgments
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.
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. https://doi.org/10.1214/24-ECP585
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