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Central limit theorem for partial linear eigenvalue statistics of Wigner matrices
Central limit theorem partial linear eigenvalue statistics Wigner matrices Probability
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2012/6/19
In this paper, we study the complex Wigner matrices $M_n=\frac{1}{\sqrt{n}}W_n$ whose eigenvalues are typically in the interval $[-2,2]$. Let $\lambda_1\leq \lambda_2...\leq\lambda_n$ be the ordered e...
New estimators of spectral distributions of Wigner matrices
Wigner matrices Stieltjes transform nonparametric estimate domain of attraction of normal law
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2011/9/6
Abstract: We introduce kernel estimators for the semicircle law. In this first part of our general theory on the estimators, we prove the consistency and conduct simulation study to show the performan...
Spectral Properties of Wigner Matrices
Spectral Properties Wigner Matrices
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2010/12/13
In these notes we review recent progress (and, in Section 5, we announce a new result) oncerning the statistical properties of the spectrum of Wigner random matrices.
Asymptotes in $SU(2)$ Recoupling Theory: Wigner Matrices, $3j$ Symbols, and Character Localization
SU(2) representation theory semiclassical analysis
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2010/12/14
In this paper we employ a novel technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index...