# Spectral statistics for random Schr\"odinger operators in the localized regime

@article{Germinet2010SpectralSF, title={Spectral statistics for random Schr\"odinger operators in the localized regime}, author={Franccois Germinet and Fr{\'e}d{\'e}ric Klopp}, journal={arXiv: Spectral Theory}, year={2010} }

We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume the density of states function is not too flat near $E$. Restrict it to some large cube $\Lambda$. Consider now $I_\Lambda$, a small energy interval centered at $E$ that asymptotically contains infintely many eigenvalues when the volume of the cube $\Lambda$ grows to infinity. We prove that, with…

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