Supersymmetry applied to the spectrum edge of random matrix ensembles

A new matrix ensemble has recently been proposed to describe the transport properties in mesoscopic quantum wires. Both analytical and numerical studies have shown that the ensemble of Laguerre or of chiral random matrices provides a good description of scattering properties in this class of systems. Until now only conventional methods of random matrix theory have been used to study statistical properties within this ensemble. We demonstrate that the supersymmetry method, already employed in the study Dyson ensembles, can be extended to treat this class of random matrix ensembles. In developing this approach we investigate both new, as well as verify known statistical measures. Although we focus on ensembles in which T-invariance is violated our approach lays the foundation for future studies of T-invariant systems. ((orig.))