FAST TRACK COMMUNICATION: Integral formulae for the eigenvalue density of complex random matrices
Abstract
We show that the density of complex eigenvalues for unitary invariant ensembles of complex matrices A can be written as an integral over the eigenvalues g_{j} of AA†. For the standard random matrix ensembles with matrix density of the form ∏_{j}w(g_{j}), this integral can be further reduced to a twofold integral involving the ChristoffelDarboux kernel for the orthogonal polynomials associated with weight w.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 November 2009
 DOI:
 10.1088/17518113/42/46/462002
 Bibcode:
 2009JPhA...42T2002W