On Absolute Moments of Characteristic Polynomials of a Certain Class of Complex Random Matrices
Abstract
The integer moments of the spectral determinant | det (zI − W) |2 of complex random matrices W are obtained in terms of the characteristic polynomial of the positive-semidefinite matrix WW† for the class of matrices W = AU, where A is a given matrix and U is random unitary. This work is motivated by studies of complex eigenvalues of random matrices and potential applications of the obtained results are discussed in this context.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- August 2007
- DOI:
- 10.1007/s00220-007-0270-y
- arXiv:
- arXiv:math-ph/0602032
- Bibcode:
- 2007CMaPh.273..561F
- Keywords:
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- Random Matrice;
- Random Matrix;
- Characteristic Polynomial;
- Random Matrix Theory;
- Eigenvalue Distribution;
- Mathematical Physics
- E-Print:
- 41 page, typos corrected