Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rate of Convergence to the Circular Law via Smoothing Inequalities for
  Log-Potentials   The aim of this note is to investigate the Kolmogorov distance of the
Circular Law to the empirical spectral distribution of non-Hermitian random
matrices with independent entries. The optimal rate of convergence is
determined by the Ginibre ensemble and is given by $n^{-1/2}$. A smoothing
inequality for complex measures that quantitatively relates the uniform
Kolmogorov-like distance to the concentration of logarithmic potentials is
shown. Combining it with results from Local Circular Laws, we apply it to prove
nearly optimal rate of convergence to the Circular Law in Kolmogorov distance.
Furthermore we show that the same rate of convergence holds for the empirical
measure of the roots of Weyl random polynomials.

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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: q-bio