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• W2076549096 abstract "We consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix entries. Our results generalize the previous results of [5,16,17] which constituted a key step in the proof of the local semicircle law with optimal error bound in mean-field random matrix models. Our bounds apply to random band matrices, and improve previous estimates from order 2 to order 4 in the cases relevant for applications. In particular, they lead to a proof of the diffusion approximation for the magnitude of the resolvent of random band matrices. This, in turn, implies new delocalization bounds on the eigenvectors. The applications are presented in a separate paper [3]." @default.
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• W2076549096 date "2013-02-19" @default.
• W2076549096 modified "2023-10-18" @default.
• W2076549096 title "Averaging Fluctuations in Resolvents of Random Band Matrices" @default.
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• W2076549096 doi "https://doi.org/10.1007/s00023-013-0235-y" @default.
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