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A rate of convergence for the circular law for the complex Ginibre ensemble

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 نشر من قبل Elizabeth Meckes
 تاريخ النشر 2014
  مجال البحث فيزياء
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We prove rates of convergence for the circular law for the complex Ginibre ensemble. Specifically, we bound the expected $L_p$-Wasserstein distance 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 $1 le p le 2$, the bounds are of the order $n^{-1/4}$, up to logarithmic factors.



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