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#### Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices

(Institute of Mathematical Statistics, 2009)

We consider N×N Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order 1/N. We study the connection between eigenvalue statistics on ...

#### Local Semicircle Law and Complete Delocalization for Wigner Random Matrices

(Springer Nature, 2008)

We consider N × N Hermitian random matrices with independent identical distributed entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order 1/N. Under suitable assumptions ...

#### Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation

(Institute of Mathematical Statistics, 2010)

We consider N×N Hermitian random matrices with independent identically distributed entries (Wigner matrices). We assume that the distribution of the entries have a Gaussian component with variance N−3/4+βN−3/4+β for some ...

#### Bulk universality for Wigner matrices

(Wiley-Blackwell, 2010)

We consider N × N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density ν(x) = e−U(x). We prove that the eigenvalue statistics in the bulk are given by the Dyson ...

#### Universality of random matrices and local relaxation flow

(Springer Nature, 2010)

Consider the Dyson Brownian motion with parameter β, where β=1,2,4 corresponds to the eigenvalue flows for the eigenvalues of symmetric, hermitian and quaternion self-dual ensembles. For any β≥1, we prove that the relaxation ...

#### Wegner Estimate and Level Repulsion for Wigner Random Matrices

(Oxford University Press (OUP), 2009)

We consider N × N Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing between consecutive eigenvalues is of order 1/ N. Under ...