English

Optimal multi-resolvent local laws for Wigner matrices

Probability 2022-11-02 v2 Mathematical Physics math.MP

Abstract

We 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.

Keywords

Cite

@article{arxiv.2112.13693,
  title  = {Optimal multi-resolvent local laws for Wigner matrices},
  author = {Giorgio Cipolloni and László Erdős and Dominik Schröder},
  journal= {arXiv preprint arXiv:2112.13693},
  year   = {2022}
}

Comments

34 pages

R2 v1 2026-06-24T08:32:36.513Z