Localization Transitions from Free Random Variables

We motivate and use the concept of free random variables for the studies of the de-pinning transition of flux lines in superconductors as recently discussed by Hatano and Nelson. We derive analytical conditions for the critical points of the eigenvalue distribution in the complex plane for all values of the transverse magnetic field in one-dimension, in agreement with numerical calculations. We suggest a relation between reduced nonhermitean quantum mechanics in D-dimensions and nonhermitean random matrix models with weak nonhermiticity.