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A rate of convergence for the circular law for the complex Ginibre ensemble
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 24 (2015) no. 1, pp. 93-117.

Nous établissons des vitesses de convergence pour la loi du cercle de l’ensemble de Ginibre complexe. Plus précisément, nous donnons des bornes supérieurs pour les distances de Wasserstein d’ordre p entre la mesure spectrale empirique de l’ensemble de Ginibre complexe normalisée et la mesure uniform du disque, en espérance et presque sûrement. Si 1p2, les bornes sont de la taille n -1/4 , à des facteurs logarithmiques près.

We prove rates of convergence for the circular law for the complex Ginibre ensemble. Specifically, we bound the L p -Wasserstein distances between the empirical spectral measure of the normalized complex Ginibre ensemble and the uniform measure on the unit disc, both in expectation and almost surely. For 1p2, the bounds are of the order n -1/4 , up to logarithmic factors.

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DOI : https://doi.org/10.5802/afst.1443
@article{AFST_2015_6_24_1_93_0,
     author = {Elizabeth S. Meckes and Mark W. Meckes},
     title = {A rate of convergence for the circular law for the complex {Ginibre} ensemble},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {93--117},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 24},
     number = {1},
     year = {2015},
     doi = {10.5802/afst.1443},
     mrnumber = {3325952},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1443/}
}
Elizabeth S. Meckes; Mark W. Meckes. A rate of convergence for the circular law for the complex Ginibre ensemble. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 24 (2015) no. 1, pp. 93-117. doi : 10.5802/afst.1443. https://afst.centre-mersenne.org/articles/10.5802/afst.1443/

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