scholarly journals Universality at the edge of the spectrum for unitary, orthogonal, and symplectic ensembles of random matrices

2007 ◽  
Vol 60 (6) ◽  
pp. 867-910 ◽  
Author(s):  
Percy Deift ◽  
Dimitri Gioev
Keyword(s):  
Random Matrices ◽  
Orthogonal And Symplectic Ensembles

Universality

2018 ◽  
Author(s):  
Mark Adler
Keyword(s):  
Random Matrices ◽  
Singular Points ◽  
Unitary Matrix ◽  
Edge Points ◽  
Universality Classes ◽  
Correlation Kernels ◽  
Orthogonal And Symplectic Ensembles ◽  
Matrix Ensembles ◽  
Basic Characteristics

This article deals with the universality of eigenvalue spacings, one of the basic characteristics of random matrices. It first discusses the heuristic meaning of universality before describing the standard universality classes (sine, Airy, Bessel) and their appearance in unitary, orthogonal, and symplectic ensembles. It then examines unitary matrix ensembles in more detail and shows that universality in these ensembles comes down to the convergence of the properly scaled eigenvalue correlation kernels. It also analyses the Riemann–Hilbert method, along with certain non-standard universality classes that arise at singular points in the limiting spectrum. Finally, it considers the limiting kernels for each of the three types of singular points, namely interior singular points, singular edge points, and exterior singular points.

Communication Optimal Parallel Multiplication of Sparse Random Matrices

2013 ◽  
Author(s):  
Grey Ballard ◽  
Aydin Buluc ◽  
James Demmel ◽  
Laura Grigori ◽  
Benjamin Lipshitz ◽  
...  
Keyword(s):  
Random Matrices ◽  
Sparse Random Matrices ◽  
Parallel Multiplication

VICTORIA transform, RESPECT and REFORM methods for the proof of the G-Elliptic Law under G-Lindeberg condition and twice stochastic condition for the variances and covariances of the entries of some random matrices

2020 ◽  
Vol 28 (2) ◽  
pp. 131-162
Author(s):  
Vyacheslav L. Girko
Keyword(s):  
Random Matrices ◽  
Random Matrix ◽  
Lindeberg Condition

AbstractThe G-Elliptic law under the G-Lindeberg condition for the independent pairs of the entries of a random matrix is proven.

Diagrammatic Perturbation Expansion for Ensembles of Random Matrices

1970 ◽  
Vol 11 (10) ◽  
pp. 3103-3110 ◽  
Author(s):  
J. F. McDonald ◽  
L. D. Favro
Keyword(s):  
Random Matrices ◽  
Perturbation Expansion

scholarly journals Eigenvalues and Condition Numbers of Complex Random Matrices

2004 ◽  
Vol 26 (2) ◽  
pp. 441-456 ◽  
Author(s):  
T. Ratnarajah ◽  
R. Vaillancourt ◽  
M. Alvo
Keyword(s):  
Random Matrices ◽  
Condition Numbers
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