Uniform existence of the integrated density of states for randomly   weighted Hamiltonians on long-range percolation graphs
  In this paper we consider random Hamiltonians defined on long-range percolation graphs over $\ZZ^d$. The Hamiltonian consists of a randomly weighted Laplacian plus a random potential. We prove uniform existence of the integrated density of states and express the IDS using a Pastur-Shubin trace formula. 
Slim Ayadi, Fabian Schwarzenberger, Ivan Veselic
math.SP math-ph math.MP