Tags → #local law
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Optimal multi-resolvent 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.
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Rank-uniform 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 well-known averaged and isotropic local laws.