Integrated density of states for random metrics on manifolds

Daniel Lenz , Norbert Peyerimhoff , Ivan Veselic'

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classification 🧮 math-ph math.MPmath.SP

keywords randomdensityintegratedoperatorsstatesalmostconstancycovering

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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 \v{S}ubin type trace formula.

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Integrated density of states for random metrics on manifolds

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