Uniform existence of the integrated density of states for random   Schr\"odinger operators on metric graphs over $\mathbb{Z}^d$
  We consider ergodic random magnetic Schr\"odinger operators on the metric graph $\mathbb{Z}^d$ with random potentials and random boundary conditions taking values in a finite set. We show that normalized finite volume eigenvalue counting functions converge to a limit uniformly in the energy variable. This limit, the integrated density of states, can be expressed by a closed Shubin-Pastur type trace formula. It supports the spectrum and its points of discontinuity are characterized by existence of compactly supported eigenfunctions. Among other examples we discuss percolation models. 
Michael J. Gruber, Daniel H. Lenz, Ivan Veseli\'c