Results 1 to 10 of about 52,710 (255)
The Wasserstein distance to the circular law
Annales De L'institut Henri Poincare (B) Probability and Statistics, 2023 We investigate the Wasserstein distance between the empirical spectral distribution of non-Hermitian random matrices and the Circular Law. For general entry distributions, we obtain a nearly optimal rate of convergence in 1-Wasserstein distance of order $n^{-1/2+ε}$ and we prove that the optimal rate $n^{-1/2}$ is attained by Ginibre matrices.
Jonas Jalowy
exaly +3 more sources
The circular law for random matrices
Annals of Probability, 2010 Published in at http://dx.doi.org/10.1214/09-AOP522 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Alexander N Tikhomirov +1 more
exaly +6 more sources
Annals of Probability, 1997 This paper studies the conjecture that the empirical spectral distribution of an \(n\times n\) matrix of i.i.d. entries \(\xi_{kj} =(1/ \sqrt n) x_{kj}\) and \(\{x_{kj},\;k,j=1,2, \dots\}\) forming an infinite double array of i.i.d. complex random variables converges to the uniform distribution over the unit disc on the complex plane, which is called ...
Z D Bai
exaly +3 more sources
Probability Surveys, 2012 Added: one reference and few ...
Djalil Chafai, Charles Bordenave
exaly +6 more sources
Local circular law for random matrices [PDF]
Probability Theory and Related Fields, 2013 The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of this law at any point $z$ away from the unit circle.
Paul Bourgade +2 more
exaly +6 more sources
Local inhomogeneous circular law [PDF]
Annals of Applied Probability, 2018 37 pages, 3 figures.
László Erdos +2 more
exaly +5 more sources
The local circular law II: the edge case [PDF]
Probability Theory and Related Fields, 2013 In the first part of this article, we proved a local version of the circular law up to the finest scale $N^{-1/2+ \e}$ for non-Hermitian random matrices at any point $z \in \C$ with $||z| - 1| > c $ for any $c>0$ independent of the size of the matrix.
Paul Bourgade +2 more
exaly +5 more sources
Random matrices: Universality of ESDs and the circular law
Annals of Probability, 2010 45 pages, 8 figures, submitted, Acta Math. The main article is by Tao and Vu, the appendix is by Krishnapur, and the figures are by Phillip Wood.
Terence Tao +2 more
exaly +4 more sources
Intellectual property for commercial ideas in technology markets: A system dynamics model
Journal of Open Innovation: Technology, Market and Complexity, 2023 Traditional intellectual property principles hold that ideas themselves must not be appropriated. Nevertheless, within open and collaborative dynamics, ideas are traded in technology markets for a stand-alone value.
Maria Alejandra Echavarría-Arcila +2 more
doaj +1 more source
Illegal Ministerial Circulars in Indonesia: Implications for Legitimacy
Rechtsidee: Law Journal, 2023 This normative research aimed to examine the extent of ministerial circular letters in Indonesia and whether a particular circular letter violates the Law Number 17 of 2014. Through a qualitative literature review and legal analysis, the study found that
Ari Gunawan +3 more
doaj +1 more source