Abstract. We construct an expansion in generalized eigenfunctions for Schrödinger operators on metric graphs. We require rather minimal assumptions concerning the graph structure and the boundary conditions at the vertices.

Abstract. We study spectra of alloy-type random Schrödinger 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 Schrödinger operators on metric graphs with a Z ν-structure. For certain models the two above results together imply the Lipschitz continuity of the integrated density of states. 1.

Abstract. We consider an alloy type potential on an infinite metric graph. We assume a covering condition on the single site potentials. For random Schrödingers operator associated with the alloy type potential restricted to finite volume subgraphs we prove a Wegner estimate which reproduces the modulus of continuity of the single site distribution measure. The Wegner constant is independent of the energy. 1.

Abstract. We construct an expansion in generalized eigenfunctions for Schrödinger operators on metric graphs. We require rather minimal assumptions concerning the graph structure and the boundary conditions at the vertices.