Uniform existence of the integrated density of states on metric Cayley graphs

Abstract

Given a finitely generated amenable group we consider ergodic random Schrödinger operators on a Cayley graph with random potentials and random boundary conditions. We show that the normalised eigenvalue counting functions of finite volume parts converge uniformly. The integrated density of states as the limit can be expressed by a Pastur-Shubin formula. The spectrum supports the corresponding measure and discontinuities correspond to the existence of compactly supported eigenfunctions.

17 pages, 1 figure

References in corpus (7)

• 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
• Continuity of the integrated density of states on random length metric graphs
• Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over ${\mathbb{Z}}^d$
• Eigenfunction expansion for Schrodinger operators on metric graphs
• Uniform existence of the integrated density of states for combinatorial and metric graphs over Z^d