# Spectral statistics of random band matrices and quantum unique ergodicity

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Horng-Tzer Yau , Harvard University
Fine Hall 214

We prove the universality for the eigenvalue statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable to the linear size of the matrix. By relying on a mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.