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From the mesoscopic to microscopic scale in random matrix theory

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Periodic and Ergodic Spectral Problems

Co-authors: Laszlo Erdos (IST), Horng Tzer Yau (Harvard), Jun Yin (Wisconsin Madison)

Eugene Wigner has envisioned that the distributions of the eigenvalues of large Gaussian random matrices are new paradigms for universal statistics of large correlated quantum systems. These random matrix eigenvalues statistics supposedly occur together with delocalized eigenstates. I will explain recent developments proving this paradigm for eigenvalues and eigenvectors of random matrices. This is achieved by bootstrap on scales, from mesoscopic to microscopic. Random walks in random environments, homogenization and the coupling method play a key role.

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

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