On the level density of random band matrices

1991 ◽  
Vol 50 (6) ◽  
pp. 1232-1242 ◽  
Author(s):  
L. V. Bogachev ◽  
S. A. Molchanov ◽  
L. A. Pastur
Keyword(s):  
Level Density ◽  
Band Matrices ◽  
Random Band

scholarly journals The almost sure semicircle law for random band matrices with dependent entries

2021 ◽  
Vol 131 ◽  
pp. 172-200
Author(s):  
Michael Fleermann ◽  
Werner Kirsch ◽  
Thomas Kriecherbauer
Keyword(s):  
Band Matrices ◽  
Semicircle Law ◽  
Random Band ◽  
Dependent Entries

scholarly journals Evidence of the Poisson/Gaudin–Mehta phase transition for band matrices on global scales

2018 ◽  
Vol 07 (02) ◽  
pp. 1850002
Author(s):  
Sheehan Olver ◽  
Andrew Swan
Keyword(s):  
Phase Transition ◽  
Boundary Conditions ◽  
Rate Of Convergence ◽  
Critical Behavior ◽  
Level Density ◽  
Boundary Effects ◽  
Fourth Moment ◽  
Band Matrices ◽  
Band Matrix ◽  
Symmetric Band

We prove that the Poisson/Gaudin–Mehta phase transition conjectured to occur when the bandwidth of an [Formula: see text] symmetric band matrix grows like [Formula: see text] is naturally observable in the rate of convergence of the level density to the Wigner semi-circle law. Specifically, we show for periodic and non-periodic band matrices the rate of convergence of the fourth moment of the level density is independent of the boundary conditions in the localized regime [Formula: see text] with a rate of [Formula: see text] for both cases, whereas in the delocalized regime [Formula: see text] where boundary effects become important, the rate of convergence for the two ensembles differs significantly, slowing to [Formula: see text] for non-periodic band matrices. Additionally, we examine the case of thick non-periodic band matrices [Formula: see text], showing that the fourth moment is maximally deviated from the Wigner semi-circle law when [Formula: see text], and provide numerical evidence that the eigenvector statistics also exhibit critical behavior at this point.

scholarly journals Diffusion Profile for Random Band Matrices: A Short Proof

2019 ◽  
Vol 177 (4) ◽  
pp. 666-716 ◽  
Author(s):  
Yukun He ◽  
Matteo Marcozzi
Keyword(s):  
Short Proof ◽  
Diffusion Profile ◽  
Band Matrices ◽  
Random Band

scholarly journals Universality for 1d Random Band Matrices: Sigma-Model Approximation

2018 ◽  
Vol 172 (2) ◽  
pp. 627-664 ◽  
Author(s):  
Mariya Shcherbina ◽  
Tatyana Shcherbina
Keyword(s):  
Sigma Model ◽  
Model Approximation ◽  
Band Matrices ◽  
Random Band

scholarly journals Correlated random band matrices: Localization-delocalization transitions

2000 ◽  
Vol 61 (6) ◽  
pp. 6278-6286 ◽  
Author(s):  
Martin Janssen ◽  
Krystian Pracz
Keyword(s):  
Band Matrices ◽  
Random Band
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