A linear Wegner estimate for alloy type Schroedinger operators on metric graphs

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 $\ZZ^ν$-structure. For certain models the two above results together imply the Lipschitz continuity of the integrated density of states.

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Cited by in corpus (11)

• Scale-free unique continuation estimates and applications to random Schrödinger operators
• Scale-free unique continuation principle, eigenvalue lifting and Wegner estimates for random Schrödinger operators
• Continuity of the integrated density of states on random length metric graphs
• Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over ${\mathbb{Z}}^d$
• Continuity properties of the integrated density of states on manifolds
• Localization on quantum graphs with random vertex couplings
• Uniform existence of the integrated density of states for combinatorial and metric graphs over Z^d
• The modulus of continuity of Wegner estimates for random Schrödinger operators on metric graphs
• Localisation for Delone operators via Bernoulli randomisation
• Optimal Wegner estimates for random Schroedinger operators on metric graphs
• Anderson Localization for a Multi-Particle Quantum Graph