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Random matrices: Universality of local spectral statistics of non-Hermitian matrices
Random matrices non-Hermitian matrices Probability
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2012/6/30
It is a classical result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n \times n$ gaussian matrix with independent entries of mean zero and unit variance are asymp...
Random Walk on a Co-Compact Fuchsian Group: Behavior of the Green's Function at the Spectral Radius
hyperbolic group surface group randomwalk Green’s function Gromov boundary Martin boundary Ruelle operator theorem
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2011/9/22
Abstract: It is proved that the Green's function of a symmetric finite range random walk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence R. It is also show...
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...