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Diffusion profile and delocalization for random band matrices

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Mathematics and Physics of Anderson localization: 50 Years After

I give a summary of recent progress in establishing the diffusion approximation for random band matrices. We obtain a rigorous derivation of the diffusion profile in the regime W > N^{4/5}, where W is the band width and N the dimension of the matrix. As a corollary, we prove complete delocalization of the eigenvectors. Our proof is based on a new self-consistent equation for the Green function.

Joint work with L. Erdos, H.T. Yau, and J. Yin.

This talk is part of the Isaac Newton Institute Seminar Series series.

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