  We propose a Multi-level Monte Carlo technique to accelerate Monte Carlo
sampling for approximation of properties of materials with random defects.
  The computational efficiency is investigated on test problems given by
tight-binding models of a single layer of graphene or of $MoS_2$ where the
integrated electron density of states per unit area is taken as a
representative quantity of interest.
  For the chosen test problems the multi-level Monte Carlo estimators
significantly reduce the computational time of standard Monte Carlo estimators
to obtain a given accuracy.
