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

Understand

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 $\Lambda$.