{"_id":"59183","date_updated":"2025-03-31T07:20:09Z","issue":"03","type":"journal_article","date_created":"2025-03-31T07:12:18Z","status":"public","intvolume":"        10","author":[{"first_name":"Friedrich","last_name":"Götze","full_name":"Götze, Friedrich"},{"last_name":"Jalowy","first_name":"Jonas","full_name":"Jalowy, Jonas"}],"publisher":"World Scientific Pub Co Pte Lt","publication_identifier":{"issn":["2010-3263","2010-3271"]},"abstract":[{"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>","lang":"eng"}],"publication":"Random Matrices: Theory and Applications","doi":"10.1142/s201032632150026x","article_number":"2150026","year":"2020","volume":10,"title":"Rate of convergence to the Circular Law via smoothing inequalities for log-potentials","publication_status":"published","citation":{"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} }","short":"F. Götze, J. Jalowy, Random Matrices: Theory and Applications 10 (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>.","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>","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>.","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>.","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>"},"user_id":"113768","language":[{"iso":"eng"}]}