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Advances in mathematics (New York. 1965), ISSN 0001-8708, 2012, Volume 229, Issue 3, pp. 1435 - 1515
.... We prove that the Stieltjes transform of the empirical eigenvalue distribution of H is given by the Wigner semicircle law uniformly up to the edges of the spectrum with an error of order ( N η ) − 1 where η... 
Dyson Brownian motion | Random matrix | Tracy–Widom distribution | Local semicircle law | Tracy-Widom distribution | DELOCALIZATION | SEMICIRCLE LAW | BULK UNIVERSALITY | DISTRIBUTIONS | MATHEMATICS | RESPECT | ORTHOGONAL POLYNOMIALS | ASYMPTOTICS | SPECTRUM | EDGE
Journal Article
Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, ISSN 1350-7265, 2012, Volume 18, Issue 1, pp. 322 - 359
Journal Article
2005, Probability and its applications (Springer-Verlag), ISBN 1852338687, xiii, 228
Book
Communications on Pure and Applied Mathematics, ISSN 0010-3640, 11/2016, Volume 69, Issue 11, pp. 2131 - 2194
.... entries with variance 1/N. Under mild assumptions, as N grows the empirical distribution of the eigenvalues... 
SPECTRAL DISTRIBUTION | MATHEMATICS | UNIVERSALITY | MATHEMATICS, APPLIED | PERTURBATIONS | NORM | LIMIT | VALUES | FINITE RANK DEFORMATIONS | ZEROS | Probability | Mathematics
Journal Article
Journal of Multivariate Analysis, ISSN 0047-259X, 2006, Volume 97, Issue 6, pp. 1382 - 1408
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 06/2017, Volume 58, Issue 6, p. 63301
In this article, we study the fluctuations of linear statistics of eigenvalues of circulant, symmetric circulant, reverse circulant, and Hankel matrices... 
CIRCULANT TYPE MATRICES | TOEPLITZ | CLT | PHYSICS, MATHEMATICAL | SPECTRAL NORM | STATISTICS | Construction standards | Fluctuations | Mathematical analysis | Normal distribution | Eigenvalues | Gaussian distribution | Random variables | Hankel matrices | Statistics | Matrix methods | Eigen values | Mathematics - Probability
Journal Article
Boundary Value Problems, ISSN 1687-2762, 12/2018, Volume 2018, Issue 1, pp. 1 - 6
.... By taking Dirichlet eigenvalues into account, given a certain weight function ω, we will show the minimizer of the mth eigenvalue is the m-degree continuous symmetrical decreasing rearrangement of ω... 
Ordinary Differential Equations | Analysis | Difference and Functional Equations | Approximations and Expansions | Distribution function | Equimeasurable | Eigenvalue | Mathematics, general | Mathematics | Partial Differential Equations | Rearrangement | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | Eigenvalues | Dirichlet problem | Weighting functions | Eigen values
Journal Article
International Journal of Modern Physics A, ISSN 0217-751X, 01/2015, Volume 30, Issue 1, p. 1450197
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 3/2019, Volume 32, Issue 1, pp. 353 - 394
... . Assuming m depends on n, by using the special structures of the eigenvalues we developed, explicit limits of spectral distributions are obtained regardless of the speed of m compared to n... 
Primary 15B52 | 60G55 | Eigenvalue | Probability Theory and Stochastic Processes | Mathematics | Empirical distribution | Statistics, general | Determinantal point process | 62H10 | Non-symmetric random matrix | Secondary 60F99 | MATRICES | STATISTICS & PROBABILITY | ENTRIES
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 04/2008, Volume 77, Issue 4, p. 041108
...) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary, and symplectic ensembles... 
DISTRIBUTIONS | POLYNUCLEAR GROWTH-MODEL | LANDSCAPE | PHYSICS, FLUIDS & PLASMAS | STATIONARY-POINTS | FLUCTUATIONS | ENERGY LEVELS | PHYSICS, MATHEMATICAL | Physics - Statistical Mechanics | Condensed Matter | Physics | Statistical Mechanics
Journal Article
Physical review letters, ISSN 1079-7114, 2006, Volume 97, Issue 16, p. 160201
Journal Article
PLoS ONE, ISSN 1932-6203, 09/2014, Volume 9, Issue 9, p. e106052
Journal Article
Annals of Statistics, ISSN 0090-5364, 08/2017, Volume 45, Issue 4, pp. 1609 - 1637
In this paper, we consider the extreme behavior of the extremal eigenvalues of white Wishart matrices, which plays an important role in multivariate analysis... 
β-Laguerre ensemble | Random matrix | Extremal eigenvalues | Importance sampling | random matrix | MONTE-CARLO | DISTRIBUTIONS | extremal eigenvalues | beta-Laguerre ensemble | STATISTICS & PROBABILITY | SIMULATION
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 04/2011, Volume 83, Issue 4, p. 041105
Journal Article