Complex random matrix models with possible applications to spin-impurity scattering in quantum Hall fluids
We study the one-point and two-point Green functions in a complex random matrix model to sub-leading orders in the large- N limit. We take this complex matrix model as a model for the two-state scattering problem, as applied to spin-dependent scattering of impurities in quantum Hall fluids. The density of state shows a singularity at the band center due to reflection symmetry. We also compute the one-point Green function for a generalized situation by putting random matrices on a lattice of arbitrary dimensions.