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.
Cipolloni, G., Erdős, L., Schroeder, D. (2022). Optimal multi-resolvent local laws for Wigner matrices. ELECTRONIC JOURNAL OF PROBABILITY, 27, 1-38 [10.1214/22-EJP838].
Optimal multi-resolvent local laws for Wigner matrices
Cipolloni, Giorgio;
2022-01-01
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.File in questo prodotto:
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