Spectral Statistics for the Discrete Anderson Model in the Localized Regime

نویسنده

  • FRÉDÉRIC KLOPP
چکیده

We report on recent results on the spectral statistics of the discrete Anderson model in the localized phase obtained in [6]. In particular, we describe the • locally uniform Poisson behavior of the rescaled eigenvalues, • independence of the Poisson processes obtained as such limits at distinct energies, • locally uniform Poisson behavior of the joint distributions of the rescaled energies and rescaled localization centers in a large range of scales. • the distribution of the rescaled level spacings, locally and globally in energy, • the distribution of the rescaled localization centers spacings. Our results show, in particular, that, for the discrete Anderson Hamiltonian with smoothly distributed random potential at sufficiently large coupling, the limit of the level spacing distribution is that of i.i.d. random variables distributed according to the density of states of the random Hamiltonian.

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تاریخ انتشار 2010