Linear Wegner estimate for alloy-type Schrodinger operators on metric graphs

We study spectra of alloy-type random Schrodinger operators on metric graphs. For finite edge subsets we prove a Wegner estimate which is linear in the volume (i.e., the total length of the edges) and the length of the energy interval. The single site potential needs to have fixed sign; the metric graph does not need to have a periodic structure. A further result is the existence of the integrated density of states for ergodic random Hamiltonians on metric graphs with a Z(nu) structure. For certain models the two above results together imply the Lipschitz continuity of the integrated density of states. (c) 2007 American Institute of Physics.