Explicit finite volume criteria for localization in continuous random media and applications

We give finite volume criteria for localization of quantum or classicalwaves in continuous random media. We provide explicit conditions,depending on the parameters of the model, for starting the bootstrapmultiscale analysis. A simple application to Anderson Hamiltonianson the continuum yields localization at the bottom of the spectrumin an interval of size C for large , where stands for the disorderparameter. A more sophisticated application proves localization fortwo-dimensional random Schrödinger operators in a constant magneticfield (random Landau Hamiltonians) up to a distance from the Landau levels for large B, where B is the strength of themagnetic field.