Abstract
We investigate the Wasserstein distance between the empirical spectral distribution of non-Hermitian random matrices and the circular law. For Ginibre matrices, we obtain an optimal rate of convergence
Nous étudions la distance de Wasserstein entre la distribution spectrale empirique des matrices aléatoires non hermitiennes et la loi circulaire. Pour les matrices de Ginibre, nous obtenons un taux de convergence optimal
Funding Statement
Supported by the German Research Foundation (DFG) through the SPP 2265 Random Geometric Systems.
Acknowledgments
I would like to thank Anna Gusakova, Martin Huesmann and Matthias Erbar for helpful discussions and valuable suggestions. Furthermore, I thank the referees for reading the manuscript so thoroughly and for all their great feedback.
Citation
Jonas Jalowy. "The Wasserstein distance to the circular law." Ann. Inst. H. Poincaré Probab. Statist. 59 (4) 2285 - 2307, November 2023. https://doi.org/10.1214/22-AIHP1317
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