Localization transitions from free random variables

We motivate and use the concept of free random variables for the study of t he de-pinning transition of Aux lines in superconductors as recently discus sed by Hatano and Nelson in one dimension. Our analysis yields naturally to a generalization of the concept of Coherent Phase Appproximation (CPA) for nonhermitean Hamiltonians, and is exact for Cauchy randomness. We derive a nalytical conditions for the critical points of the complex eigenvalue dist ribution, in very good agreement with numerical calculations. We suggest a relation between dimensionally reduced nonhermitean quantum mechanics and w eak nonhermiticity.