Anisotropic local laws for random matrices

Our main result is a local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices, modeled on the local semicircle law.. Our approach

GUE, GOE, GSE for the case of Hermitian, symmetric, and, respectively, quaternion self-dual Wigner matrices; and the ensembles of real or complex sample covariance matrices

The object of this work is to give a new method for proving Sinai’s theorem; this method is sufficiently general to be easily adapted to prove a similar local limit theorem in

This dispersion was proved in the case of rotating fluids ([12], [29]) or in the case of primitive equations ([9]) in the form of Strichartz type estimates, which allows to prove

[33] G.M. Zhou, Circular law, extreme singular values and potential theory, J. Vershynin, The Littlewood-Offord problem and invertibility of random matrices, Adv. Totik,

In Section 5, we perform step (B) of the proof by proving the anisotropic local law in Theorem 2.18 using the entrywise local law proved in Section 4.. Finally in Section 6 we

In the first part of this article [8], we proved a local version of the circular law up to the finest scale N −1/2+ε for non-Hermitian random matrices at any point z ∈ C with || z |

Let H = (N −1/2 X ij ) be an arbitrary real symmetric / complex Hermitian Wigner matrix and (N −1/2 Y ij ) a GOE/GUE matrix independent of H.. Provided ρ is a large enough constant,