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Quantum chaos on discrete graphs

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If you have a question about this talk, please contact Mustapha Amrani.

Mathematics and Physics of Anderson localization: 50 Years After

The spectral statistics of the discrete Laplacian on random d-regular graphs (in the limit of large graphs), will be discussed. It will be shown that in this limit some spectral statistics follow the predictions of Random Matrix Theory. Counting statistics of cycles on the graphs play an important role in the analysis. The level sets of eigenvectors will be shown to display a percollation transition which can be proved by assuming that eigenvectors distribute normally, with a covariance which can be computed using the special properties of the random ensemble of large d-regular graphs.

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

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