Poisson statistics for 1d Schr\"odinger operators with random decaying   potentials
  We consider the 1d Schr\"odinger operators with random decaying potentials where the spectrum is pure point(sub-critical case). We show that the point process composed of the rescaled eivenvalues, together with those zero points of the corresponding eigenfunctions, converges to the Poisson process. 
Shinichi Kotani and Fumihiko Nakano
math-ph math.MP math.PR