Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices

Alexander D. Mirlin, Yan V. Fyodorov, Frank-Michael Dittes +2

We study statistical properties of the ensemble of large $N\times N$ random matrices whose entries $H_{ij}$ decrease in a power-law fashion $H_{ij}\sim |i-j{|}^{-\alpha }$. Mapping the pro…