scholarly journals Parametric spectral statistics in unitary random matrix ensembles: from distribution functions to intra-level correlations

2003 ◽  
Vol 36 (12) ◽  
pp. 3551-3567 ◽  
Author(s):  
I E Smolyarenko ◽  
B D Simons
Keyword(s):  
Random Matrix ◽  
Distribution Functions ◽  
Spectral Statistics ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles

scholarly journals Spectral statistics of non-Hermitian random matrix ensembles

2019 ◽  
Vol 08 (02) ◽  
pp. 1950005
Author(s):  
Ryan C. Chen ◽  
Yujin H. Kim ◽  
Jared D. Lichtman ◽  
Steven J. Miller ◽  
Shannon Sweitzer ◽  
...  
Keyword(s):  
Complex Plane ◽  
Random Matrix ◽  
Moment Method ◽  
Singular Values ◽  
Limiting Behavior ◽  
Complex Eigenvalues ◽  
Spectral Statistics ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles ◽  
Gaussian Ensembles

Recently Burkhardt et al. introduced the [Formula: see text]-checkerboard random matrix ensembles, which have a split limiting behavior of the eigenvalues (in the limit all but [Formula: see text] of the eigenvalues are on the order of [Formula: see text] and converge to semi-circular behavior, with the remaining [Formula: see text] of size [Formula: see text] and converging to hollow Gaussian ensembles). We generalize their work to consider non-Hermitian ensembles with complex eigenvalues; instead of a blip new behavior is seen, ranging from multiple satellites to annular rings. These results are based on moment method techniques adapted to the complex plane as well as analysis of singular values.

Spectral statistics in semiclassical random-matrix ensembles

1991 ◽  
Vol 66 (8) ◽  
pp. 986-989 ◽  
Author(s):  
Mario Feingold ◽  
David M. Leitner ◽  
Michael Wilkinson
Keyword(s):  
Random Matrix ◽  
Spectral Statistics ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles

Level Spacing Distributions of Random Matrix Ensembles

1993 ◽  
Vol 62 (7) ◽  
pp. 2248-2259 ◽  
Author(s):  
Masahiro Shiroishi ◽  
Taro Nagao ◽  
Miki Wadati
Keyword(s):  
Random Matrix ◽  
Level Spacing ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles

scholarly journals Gaussian perturbations of hard edge random matrix ensembles

Nonlinearity ◽  
2016 ◽  
Vol 29 (11) ◽  
pp. 3385-3416 ◽  
Author(s):  
Tom Claeys ◽  
Antoine Doeraene
Keyword(s):  
Random Matrix ◽  
Hard Edge ◽  
Random Matrix Ensembles ◽  
Matrix Ensembles
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