Add to ORKGWe prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale.Comment: 34 page
We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with ce...
We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of...
We extend the proof of the local semicircle law for generalized Wigner matrices given in MR3068390 t...
We consider sample covariance matrices of the form X ∗X, where X is an M × N matrix with independent...
We consider sample covariance matrices of the form X∗X, where X is an M×N matrix with independent ra...
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove lo...
We study Hermitian non-commutative quadratic polynomials of multiple independent Wigner matrices. We...
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove lo...
We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with ce...
We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with ce...
We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of s...
We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of s...
We consider large random matrices with a general slowly decaying correlation among its entries. We p...
We consider large random matrices with a general slowly decaying correlation among its entries. We p...
We consider large random matrices with a general slowly decaying correlation among its entries. We p...
We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with ce...
We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of...
We extend the proof of the local semicircle law for generalized Wigner matrices given in MR3068390 t...
We consider sample covariance matrices of the form X ∗X, where X is an M × N matrix with independent...
We consider sample covariance matrices of the form X∗X, where X is an M×N matrix with independent ra...
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove lo...
We study Hermitian non-commutative quadratic polynomials of multiple independent Wigner matrices. We...
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove lo...
We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with ce...
We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with ce...
We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of s...
We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of s...
We consider large random matrices with a general slowly decaying correlation among its entries. We p...
We consider large random matrices with a general slowly decaying correlation among its entries. We p...
We consider large random matrices with a general slowly decaying correlation among its entries. We p...
We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with ce...
We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of...
We extend the proof of the local semicircle law for generalized Wigner matrices given in MR3068390 t...