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We study the spectrum of a random Schroedinger operator for an electronsubmitted to a magnetic field in a finite but macroscopic two dimensionalsystem of linear dimensions equal to L. The y direction is periodic and in thex direction the electron is confined by two smooth increasing boundarypotentials. The eigenvalues of the Hamiltonian are classified according totheir associated quantum mechanical current in the y direction. Here we look atan interval of energies inside the first Landau band of the random operator forthe infinite plane. In this energy interval, with large probability, thereexist O(L) eigenvalues with positive or negative currents of O(1). Between eachof these there exist O(L^2) eigenvalues with infinitesimal currentO(exp(-cB(log L)^2)). We explain what is the relevance of this analysis to theinteger quantum Hall effect.Comment: 29 pages, no figure

Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems