On permanental polynomials of certain random matrices
arXiv:math-ph/0602039
Abstract
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.
published version, a few misprints are corrected. 34 pages, no figures
References in corpus (11)
- Products and Ratios of Characteristic Polynomials of Random Hermitian Matrices
- Supersymmetry for Systems with Unitary Disorder: Circular Ensembles
- On the averages of characteristic polynomials from classical groups
- Characteristic polynomials of real symmetric random matrices
- Characteristic polynomials of random Hermitian matrices and Duistermaat-Heckman localisation on non-compact Kaehler manifolds
- Howe pairs, supersymmetry, and ratios of random characteristic polynomials for the unitary groups U(N)
- Concentration of permanent estimators for certain large matrices
- Supersymmetric Quenching of the Toda Lattice Equation
- A simple formula for Bose-Einstein corrections
- Tau Functions and Matrix Integrals
- Giambelli compatible point processes