Optimal Wegner estimates for random Schroedinger operators on metric graphs

Abstract

We consider Schroedinger operators with a random potential of alloy type on infinite metric graphs which obey certain uniformity conditions. For single site potentials of fixed sign we prove that the random Schroedinger operator restricted to a finite volume subgraph obeys a Wegner estimate which is linear in the volume and reproduces the modulus of continuity of the single site distribution. This improves and unifies earlier results for alloy type models on metric graphs. We discuss applications of Wegner estimates to bounds of the modulus of continuity of the integrated density of states of ergodic Schroedinger operators, as well as to the proof of Anderson localisation via the multiscale analysis

LaTeX, 13 pages (a4wide); minor corrections

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Cited by in corpus (3)

• Continuity of the integrated density of states on random length metric graphs
• Localization on quantum graphs with random edge lengths
• Uniform existence of the integrated density of states for combinatorial and metric graphs over Z^d