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• W3102939586 startingPage "367" @default.
• W3102939586 abstract "We consider Hermitian and symmetric random band matrices H = (h xy ) in $${d,geqslant,1}$$ dimensions. The matrix entries h xy , indexed by $${x,y in (mathbb{Z}/Lmathbb{Z})^d}$$ , are independent, centred random variables with variances $${s_{xy} = mathbb{E} |h_{xy}|^2}$$ . We assume that s xy is negligible if |x − y| exceeds the band width W. In one dimension we prove that the eigenvectors of H are delocalized if $${Wgg L^{4/5}}$$ . We also show that the magnitude of the matrix entries $${|{G_{xy}}|^2}$$ of the resolvent $${G=G(z)=(H-z)^{-1}}$$ is self-averaging and we compute $${mathbb{E} |{G_{xy}}|^2}$$ . We show that, as $${Ltoinfty}$$ and $${Wgg L^{4/5}}$$ , the behaviour of $${mathbb{E} |G_{xy}|^2}$$ is governed by a diffusion operator whose diffusion constant we compute. Similar results are obtained in higher dimensions." @default.
• W3102939586 created "2020-11-23" @default.
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• W3102939586 date "2013-07-26" @default.
• W3102939586 modified "2023-10-18" @default.
• W3102939586 title "Delocalization and Diffusion Profile for Random Band Matrices" @default.
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• W3102939586 doi "https://doi.org/10.1007/s00220-013-1773-3" @default.
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