CLT for Linear Spectral Statistics

2009 ◽  
pp. 223-329
Author(s):  
Zhidong Bai ◽  
Jack W. Silverstein
Keyword(s):  
Spectral Statistics

scholarly journals Chaos on the hypercube

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yiyang Jia ◽  
Jacobus J. M. Verbaarschot
Keyword(s):  
Magnetic Flux ◽  
Spectral Density ◽  
Hermite Polynomials ◽  
Weighted Sums ◽  
Majorana Fermions ◽  
Chord Diagrams ◽  
Magnetic Inversion ◽  
Constant Magnitude ◽  
Kitaev Model ◽  
Spectral Statistics

Abstract We analyze the spectral properties of a d-dimensional HyperCubic (HC) lattice model originally introduced by Parisi. The U(1) gauge links of this model give rise to a magnetic flux of constant magnitude ϕ but random orientation through the faces of the hypercube. The HC model, which also can be written as a model of 2d interacting Majorana fermions, has a spectral flow that is reminiscent of Maldacena-Qi (MQ) model, and its spectrum at ϕ = 0, actually coincides with the coupling term of the MQ model. As was already shown by Parisi, at leading order in 1/d, the spectral density of this model is given by the density function of the Q-Hermite polynomials, which is also the spectral density of the double-scaled Sachdev-Ye-Kitaev model. Parisi demonstrated this by mapping the moments of the HC model to Q-weighted sums on chord diagrams. We point out that the subleading moments of the HC model can also be mapped to weighted sums on chord diagrams, in a manner that descends from the leading moments. The HC model has a magnetic inversion symmetry that depends on both the magnitude and the orientation of the magnetic flux through the faces of the hypercube. The spectrum for fixed quantum number of this symmetry exhibits a transition from regular spectra at ϕ = 0 to chaotic spectra with spectral statistics given by the Gaussian Unitary Ensembles (GUE) for larger values of ϕ. For small magnetic flux, the ground state is gapped and is close to a Thermofield Double (TFD) state.

scholarly journals From closed to open one-dimensional Anderson model: Transport versus spectral statistics

2012 ◽  
Vol 86 (1) ◽  
Author(s):  
S. Sorathia ◽  
F. M. Izrailev ◽  
V. G. Zelevinsky ◽  
G. L. Celardo
Keyword(s):  
Anderson Model ◽  
One Dimensional ◽  
Spectral Statistics

scholarly journals Transitions in spectral statistics

1994 ◽  
Vol 27 (16) ◽  
pp. L563-L568 ◽  
Author(s):  
C Blecken ◽  
Y Chen ◽  
K A Muttalib
Keyword(s):  
Spectral Statistics

scholarly journals Model of Quantum Chaotic Billiards: Spectral Statistics and Wave Functions in Two Dimensions

1996 ◽  
Vol 77 (10) ◽  
pp. 1970-1973 ◽  
Author(s):  
E. Cuevas ◽  
E. Louis ◽  
J. A. Vergés
Keyword(s):  
Two Dimensions ◽  
Wave Functions ◽  
Spectral Statistics ◽  
Chaotic Billiards

scholarly journals Long-Term Spectral Statistics for Voice Presentation Attack Detection

2017 ◽  
Vol 25 (11) ◽  
pp. 2098-2111 ◽  
Author(s):  
Hannah Muckenhirn ◽  
Pavel Korshunov ◽  
Mathew Magimai-Doss ◽  
Sebastien Marcel
Keyword(s):  
Attack Detection ◽  
Spectral Statistics ◽  
Presentation Attack Detection

scholarly journals Level curvatures, spectral statistics and scaling for interacting particles

1998 ◽  
Vol 1 (2) ◽  
pp. 223-227 ◽  
Author(s):  
E. Akkermans ◽  
J.-L. Pichard
Keyword(s):  
Interacting Particles ◽  
Spectral Statistics

scholarly journals Spectral statistics of rectangular billiards with localized perturbations

Nonlinearity ◽  
2002 ◽  
Vol 15 (5) ◽  
pp. 1541-1594 ◽  
Author(s):  
Saar Rahav ◽  
Shmuel Fishman
Keyword(s):  
Spectral Statistics
Sign in / Sign up

Export Citation Format

Share Document