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Localisation for random block operators

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Mathematics and Physics of Anderson localization: 50 Years After

We study spectral properties of random block operators that are common in the physical modelling of mesoscopic disordered systems such as dirty superconductors. Our results include ergodic properties, the location of the spectrum, existence and regularity of the integrated density of states (Wegner estimate), Lifshits tails and dynamical localisation in a neighbourhood of the internal band edges. Special attention is paid to the peculiarities arising from the block structure. Technically, one has to cope with a non-monotone dependence on the random couplings.

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

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