---
_id: '59183'
abstract:
- lang: eng
  text: '<jats:p> The aim of this paper 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 [Formula: see text]. 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. </jats:p>'
article_number: '2150026'
author:
- first_name: Friedrich
  full_name: Götze, Friedrich
  last_name: Götze
- first_name: Jonas
  full_name: Jalowy, Jonas
  id: '113768'
  last_name: Jalowy
  orcid: 0000-0001-9624-2685
citation:
  ama: 'Götze F, Jalowy J. Rate of convergence to the Circular Law via smoothing inequalities
    for log-potentials. <i>Random Matrices: Theory and Applications</i>. 2020;10(03).
    doi:<a href="https://doi.org/10.1142/s201032632150026x">10.1142/s201032632150026x</a>'
  apa: 'Götze, F., &#38; Jalowy, J. (2020). Rate of convergence to the Circular Law
    via smoothing inequalities for log-potentials. <i>Random Matrices: Theory and
    Applications</i>, <i>10</i>(03), Article 2150026. <a href="https://doi.org/10.1142/s201032632150026x">https://doi.org/10.1142/s201032632150026x</a>'
  bibtex: '@article{Götze_Jalowy_2020, title={Rate of convergence to the Circular
    Law via smoothing inequalities for log-potentials}, volume={10}, DOI={<a href="https://doi.org/10.1142/s201032632150026x">10.1142/s201032632150026x</a>},
    number={032150026}, journal={Random Matrices: Theory and Applications}, publisher={World
    Scientific Pub Co Pte Lt}, author={Götze, Friedrich and Jalowy, Jonas}, year={2020}
    }'
  chicago: 'Götze, Friedrich, and Jonas Jalowy. “Rate of Convergence to the Circular
    Law via Smoothing Inequalities for Log-Potentials.” <i>Random Matrices: Theory
    and Applications</i> 10, no. 03 (2020). <a href="https://doi.org/10.1142/s201032632150026x">https://doi.org/10.1142/s201032632150026x</a>.'
  ieee: 'F. Götze and J. Jalowy, “Rate of convergence to the Circular Law via smoothing
    inequalities for log-potentials,” <i>Random Matrices: Theory and Applications</i>,
    vol. 10, no. 03, Art. no. 2150026, 2020, doi: <a href="https://doi.org/10.1142/s201032632150026x">10.1142/s201032632150026x</a>.'
  mla: 'Götze, Friedrich, and Jonas Jalowy. “Rate of Convergence to the Circular Law
    via Smoothing Inequalities for Log-Potentials.” <i>Random Matrices: Theory and
    Applications</i>, vol. 10, no. 03, 2150026, World Scientific Pub Co Pte Lt, 2020,
    doi:<a href="https://doi.org/10.1142/s201032632150026x">10.1142/s201032632150026x</a>.'
  short: 'F. Götze, J. Jalowy, Random Matrices: Theory and Applications 10 (2020).'
date_created: 2025-03-31T07:12:18Z
date_updated: 2025-04-23T14:38:18Z
doi: 10.1142/s201032632150026x
intvolume: '        10'
issue: '03'
language:
- iso: eng
publication: 'Random Matrices: Theory and Applications'
publication_identifier:
  issn:
  - 2010-3263
  - 2010-3271
publication_status: published
publisher: World Scientific Pub Co Pte Lt
status: public
title: Rate of convergence to the Circular Law via smoothing inequalities for log-potentials
type: journal_article
user_id: '113768'
volume: 10
year: '2020'
...