Complex Wishart matrices and conductance in mesoscopic systems: Exact results

Abstract

It is noted that the hypothesis of independent random complex elements for the off diagonal blocks (say, M2 and M3) of the transfer matrix describing conductance in a mesoscopic wire allows the eigenvalue distribution of the matrix product M3†M3 (or M2†M2) to be computed exactly. Exact expressions, in terms of double Wronskian and Toeplitz determinants, are derived for the distribution of the smallest and second smallest eigenvalue of this and similar random matrix products. © 1994 American Institute of Physics.