Partition function and the density of states for an electron in the plane subjected to a random potential and a magnetic field

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Abstract
The object of the study is the random Landau model, that is, the Schrödinger operator in two dimensions with a perpendicular constant magnetic field and a random potential. With the help of upper and lower bounds the averaged partition function, either unrestricted or restricted to the Hilbert space of the nth Landau level, is discussed. Based on the lower bounds, approximations to the corresponding densities of states are proposed. For Gaussian random potentials the leading low-energy behavior of the unrestricted density of states is derived.

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