Integrated density of states for random metrics on manifolds

Abstract

We study ergodic random Schr"odinger operators on a covering manifold, where the randomness enters both via the potential and the metric. We prove measurability of the random operators, almost sure constancy of their spectral properties, the existence of a selfaveraging integrated density of states and a Šubin type trace formula.

21 pages

Cited by in corpus (11)

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• Low lying spectrum of weak-disorder quantum waveguides
• A linear Wegner estimate for alloy type Schroedinger operators on metric graphs
• Quantum Hamiltonians with weak random abstract perturbation. I. Initial length scale estimate
• Quantum Hamiltonians with weak random abstract perturbation. II. Localization in the expanded spectrum
• Uniform existence of the integrated density of states on metric Cayley graphs
• A General Dixmier Trace Formula for the Density of States on Open Manifolds