Tags → #local law

Optimal multiresolvent local laws for Wigner matrices
We prove local laws for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. Our key finding is that the size of such products heavily depends on whether some of the deterministic matrices are traceless.

Rankuniform local law for Wigner matrices
We prove a general local law for Wigner matrices which optimally handles observables of arbitrary rank and thus it unifies the wellknown averaged and isotropic local laws.