The modulus of continuity of Wegner estimates for random Schrödinger operators on metric graphs

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.

8 pages

References in corpus (4)

• Localization on a quantum graph with a random potential on the edges
• Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over ${\mathbb{Z}}^d$
• The Integrated Density of States for Random Schroedinger Operators
• A linear Wegner estimate for alloy type Schroedinger operators on metric graphs

Cited by in corpus (6)

• Leaky Quantum Graphs: A Review
• 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
• Uniform existence of the integrated density of states for combinatorial and metric graphs over Z^d
• Optimal Wegner estimates for random Schroedinger operators on metric graphs