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Eigenvalues
Probability Measure
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Bulk universality for generalized Wigner matrices
Bulk universality for generalized Wigner matrices,Laszlo Erdos,HorngTzer Yau,Jun Yin
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Bulk universality for generalized Wigner matrices
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Citations: 9
)
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Laszlo Erdos
,
HorngTzer Yau
,
Jun Yin
Consider $N\times N$ Hermitian or symmetric
random matrices
$H$ where the distribution of the $(i,j)$ matrix element is given by a
probability measure
$\nu_{ij}$ with a subexponential decay. Let $\sigma_{ij}^2$ be the variance for the
probability measure
$\nu_{ij}$ with the normalization property that $\sum_{i} \sigma^2_{ij} = 1$ for all $j$. Under essentially the only condition that $c\le N \sigma_{ij}^2 \le c^{1}$ for some constant $c>0$, we prove that, in the limit $N \to \infty$, the eigenvalue spacing statistics of $H$ in the bulk of the
spectrum
coincide with those of the Gaussian unitary or orthogonal ensemble (GUE or GOE). We also show that for band matrices with bandwidth $M$ the local semicircle law holds to the energy scale $M^{1}$.
Published in 2010.
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Citation Context
(1)
...In [
7
], Erd˝ os, Yau, and Yin used different methods to prove an analogue of (6) for finite band matrices of size N × N ,f or� W −1 log C N , and with error term (W �) −1/2 log C N ...
Sasha Sodin
.
An Estimate for the Average Spectral Measure of Random Band Matrices
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(31)
A CLT for a band matrix model
(
Citations: 51
)
Greg W. Anderson
,
Ofer Zeitouni
Journal:
Probability Theory and Related Fields  PROBAB THEORY RELAT FIELD
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Universality of local eigenvalue statistics for some sample covariance matrices
(
Citations: 26
)
Gérard Ben Arous
,
Sandrine Péché
Journal:
Communications on Pure and Applied Mathematics  COMMUN PURE APPL MATH
, vol. 58, no. 10, pp. 13161357, 2005
Semiclassical asymptotics of orthogonal polynomials, RiemannHilbert problem, and universality in the matrix model
(
Citations: 153
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Pavel Bleher
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Alexander Its
Published in 1999.
Exponential Integrability And Transportation Cost Related To Logarithmic Sobolev Inequalities
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S. g. Bobkov
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Published in 1997.
CORRELATIONS OF NEARBY LEVELS INDUCED BY A RANDOM POTENTIAL
(
Citations: 31
)
E. Brezina
,
Ecole Normale
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Citations
(9)
The WignerDysonMehta bulk universality conjecture for Wigner matrices
(
Citations: 1
)
Terence Tao
,
Van Vu
Published in 2011.
Myocardial Ischemia and Ventricular Tachycardia on Continuous Electrocardiographic Monitoring and Risk of Cardiovascular Outcomes After Non–STSegment Elevation Acute Coronary Syndrome (from the MERLINTIMI 36 Trial)
James R. Harkness
,
David A. Morrow
,
Eugene Braunwald
,
Fang Ren
,
J. LopezSendon
,
Christopher Bode
,
Andrzej Budaj
,
Benjamin M. Scirica
Journal:
American Journal of Cardiology  AMER J CARDIOL
, vol. 108, no. 10, pp. 13731381, 2011
An Estimate for the Average Spectral Measure of Random Band Matrices
Sasha Sodin
Journal:
Journal of Statistical Physics  J STATIST PHYS
, vol. 144, no. 1, pp. 4659, 2011
Universality for generalized Wigner matrices with Bernoulli distribution
(
Citations: 7
)
László Erdos
,
HorngTzer Yau
,
Jun Yin
Published in 2010.
Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model
(
Citations: 4
)
Laszlo Erdos
,
Antti Knowles
Published in 2010.