Dynamical mobility edge for various random Landau Hamiltonians

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We review recent results obtained within the framework of the integer quantum Hall effect in the spirit of the work of Germinet, Klein, Schenker in GKS. Landau Hamiltonians perturbed by random electric or magnetic perturbations are shown to exhibit a dynamical mobility edge, that is a transition between a regime of dynamical localization and a regime of non trivial transport at a minimal rate. The focus is put on three situations of interest: 1) unbounded ergodic electric potentials, for which Landau gaps are filled; 2) non ergodic electric potentials; 3) random magnetic potentials.