Optimal multi-resolvent local laws for Wigner matrices
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Date
2022
Publication Type
Journal Article
ETH Bibliography
yes
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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.
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published
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Journal / series
Volume
27
Pages / Article No.
117
Publisher
Institute of Mathematical Statistics
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Subject
global law; local law; random matrices