# AGA

## Seminar

### Uniform existence of the integrated density of states for random Schrodinger operators on metric graphs over Z$^d$

Lenz, D (Chemnitz)
Tuesday 03 April 2007, 15:30-16:00

Seminar Room 1, Newton Institute

#### Abstract

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.