A linear Wegner estimate for alloy type Schroedinger operators on metric graphs
Spectral Theory
2009-11-11 v1 Mathematical Physics
math.MP
Abstract
We study spectra of alloy-type random Schr\"odinger operators on metric graphs. For finite edge subsets of general graphs we prove a Wegner estimate which is linear in the volume (i.e. the number of edges) and the length of the considered energy interval. The single site potential of the alloy-type model needs to have fixed sign, but the considered metric graph does not need to have a periodic structure. The second result we obtain is an exhaustion construction of the integrated density of states for ergodic random Schr\"odinger operators on metric graphs with a -structure. For certain models the two above results together imply the Lipschitz continuity of the integrated density of states.
Cite
@article{arxiv.math/0611609,
title = {A linear Wegner estimate for alloy type Schroedinger operators on metric graphs},
author = {Mario Helm and Ivan Veselic'},
journal= {arXiv preprint arXiv:math/0611609},
year = {2009}
}