Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over $\mathbb{Z}^d$

Details Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over $\mathbb{Z}^d$ Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over $\mathbb{Z}^d$

2006-12-23

arxiv.org/abs/math/0612743v2

J. Funct. Anal. 253.2 (2007), 515--533

Mathematics

Spectral Theory

17 pages; typos removed, references updated, definition of subgraph densities explained

Scientific paper

10.1016/j.jfa.2007.09.003

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.

Affiliated with

Also associated with

No associations

Rating

Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over $\mathbb{Z}^d$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over $\mathbb{Z}^d$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over $\mathbb{Z}^d$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-380083