Scattering Theory of Schr\"{o}dinger Operators with Random Sparse   Potentials
  In this paper, we study the scattering theory of a class of continuum Schr\"{o}dinger operators with random sparse potentials. The existence and completeness of wave operators are proven by establishing the uniform boundedness of modified free resolvents and modified perturbed resolvents, and by invoking a previous result on the absence of absolutely continuous spectrum below zero. 
Zhongwei Shen
math.SP