scholarly journals Mesoscopic Linear Statistics of Wigner Matrices of Mixed Symmetry Class

2019 ◽  
Vol 175 (5) ◽  
pp. 932-959
Author(s):  
Yukun He
Keyword(s):  
Symmetry Class ◽  
Linear Statistics ◽  
Wigner Matrices ◽  
Mixed Symmetry

Limiting Behavior of Eigenvectors of Large Wigner Matrices

2011 ◽  
Vol 146 (3) ◽  
pp. 519-549 ◽  
Author(s):  
Z. D. Bai ◽  
G. M. Pan
Keyword(s):  
Limiting Behavior ◽  
Wigner Matrices

scholarly journals Equipartition principle for Wigner matrices

2021 ◽  
Vol 9 ◽  
Author(s):  
Zhigang Bao ◽  
László Erdős ◽  
Kevin Schnelli
Keyword(s):  
High Precision ◽  
Quantum Systems ◽  
Wigner Matrices ◽  
Very High

Abstract We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices.

Identification of mixed-symmetry states in odd- A 93Nb

2005 ◽  
Vol 25 (S1) ◽  
pp. 377-379 ◽  
Author(s):  
C. J. McKay ◽  
J. N. Orce ◽  
S. R. Lesher ◽  
D. Bandyopadhyay ◽  
M. T. McEllistrem ◽  
...  
Keyword(s):  
Mixed Symmetry ◽  
Mixed Symmetry States

GLOBAL FLUCTUATIONS FOR LINEAR STATISTICS OF β-JACOBI ENSEMBLES

2012 ◽  
Vol 01 (04) ◽  
pp. 1250013 ◽  
Author(s):  
IOANA DUMITRIU ◽  
ELLIOT PAQUETTE
Keyword(s):  
Gaussian Process ◽  
Covariance Matrix ◽  
Law Of Large Numbers ◽  
Test Functions ◽  
Linear Statistics ◽  
Jacobi Ensemble ◽  
Large Numbers ◽  
The Mean ◽  
Shifted Chebyshev Polynomial ◽  
Global Fluctuations

We study the global fluctuations for linear statistics of the form [Formula: see text] as n → ∞, for C1 functions f, and λ1, …, λn being the eigenvalues of a (general) β-Jacobi ensemble. The fluctuation from the mean [Formula: see text] turns out to be given asymptotically by a Gaussian process. We compute the covariance matrix for the process and show that it is diagonalized by a shifted Chebyshev polynomial basis; in addition, we analyze the deviation from the predicted mean for polynomial test functions, and we obtain a law of large numbers.

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