On permanental polynomials of certain random matrices

Details On permanental polynomials of certain random matrices On permanental polynomials of certain random matrices

2006-02-14

arxiv.org/abs/math-ph/0602039v2

International Mathematics Research Notices, vol. 2006 (2006), Article ID 61570, 37 pages

Physics

Mathematical Physics

published version, a few misprints are corrected. 34 pages, no figures

Scientific paper

The paper addresses the calculation of correlation functions of permanental polynomials of matrices with random entries. By exploiting a convenient contour integral representation of the matrix permanent some explicit results are provided for several random matrix ensembles. When compared with the corresponding formulae for characteristic polynomials, our results show both striking similarities and interesting differences. Based on these findings, we conjecture the asymptotic forms of the density of permanental roots in the complex plane for Gaussian ensembles as well as for the Circular Unitary Ensemble of large matrix dimension.

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