Uniform existence of the integrated density of states for randomly weighted Hamiltonians on long-range percolation graphs

Abstract

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.

21 pages

References in corpus (4)

• Hamiltonians on discrete structures: Jumps of the integrated density of states and uniform convergence
• Uniform existence of the integrated density of states for models on $\ZZ^d$
• A Banach space-valued ergodic theorem and the uniform approximation of the integrated density of states
• Equality of Lifshitz and van Hove exponents on amenable Cayley graphs