scholarly journals Edgeworth expansion of the largest eigenvalue distribution function of Gaussian unitary ensemble revisited

2008 ◽  
Vol 49 (3) ◽  
pp. 033508 ◽  
Author(s):  
Leonard N. Choup
Keyword(s):  
Distribution Function ◽  
Edgeworth Expansion ◽  
Eigenvalue Distribution ◽  
Largest Eigenvalue ◽  
Gaussian Unitary Ensemble ◽  
Unitary Ensemble ◽  
The Largest Eigenvalue

scholarly journals Spectral distributions of periodic random matrix ensembles

2019 ◽  
Vol 10 (01) ◽  
pp. 2150011
Author(s):  
Roger Van Peski
Keyword(s):  
Random Matrix ◽  
Spectral Distribution ◽  
Eigenvalue Distribution ◽  
Limiting Spectral Distribution ◽  
Gaussian Unitary Ensemble ◽  
Random Matrix Ensembles ◽  
Spectral Distributions ◽  
Matrix Ensembles ◽  
General Correspondence ◽  
Unitary Ensemble

Koloğlu, Kopp and Miller compute the limiting spectral distribution of a certain class of real random matrix ensembles, known as [Formula: see text]-block circulant ensembles, and discover that it is exactly equal to the eigenvalue distribution of an [Formula: see text] Gaussian unitary ensemble. We give a simpler proof that under very general conditions which subsume the cases studied by Koloğlu–Kopp–Miller, real-symmetric ensembles with periodic diagonals always have limiting spectral distribution equal to the eigenvalue distribution of a finite Hermitian ensemble with Gaussian entries which is a ‘complex version’ of a [Formula: see text] submatrix of the ensemble. We also prove an essentially algebraic relation between certain periodic finite Hermitian ensembles with Gaussian entries, and the previous result may be seen as an asymptotic version of this for real-symmetric ensembles. The proofs show that this general correspondence between periodic random matrix ensembles and finite complex Hermitian ensembles is elementary and combinatorial in nature.

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