Non-central limit theorems and convergence rates

2018 ◽  
Vol 95 ◽  
pp. 3-15 ◽  
Author(s):  
Vo Anh ◽  
Andriy Olenko ◽  
V. Vaskovych
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Convergence Rates ◽  
Central Limit Theorems

scholarly journals Fluctuations of the spectrum in rotationally invariant random matrix ensembles

2020 ◽  
pp. 2150025
Author(s):  
Elizabeth S. Meckes ◽  
Mark W. Meckes
Keyword(s):  
Central Limit ◽  
Random Matrix ◽  
Limit Theorems ◽  
Convergence Rates ◽  
Matrix Theory ◽  
Central Limit Theorems ◽  
Inner Product ◽  
Random Matrix Ensembles ◽  
Real Linear ◽  
Rotationally Invariant

We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert–Schmidt inner product) within a real-linear subspace of the space of [Formula: see text] matrices. The matrices, we consider may be real or complex, and Hermitian, antihermitian, or general. We use Stein’s method to prove multivariate central limit theorems, with convergence rates, for these traces of powers, which imply central limit theorems for polynomial linear eigenvalue statistics. In contrast to the usual situation in random matrix theory, in our approach general, nonnormal matrices turn out to be easier to study than Hermitian matrices.

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