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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/2776

Title: Characteristic polynomials in real Ginibre ensembles
Authors: Akemann, G
Phillips, M J
Sommers, H J
Publication Date: 2008
Publisher: arXiv
Citation: Journal of Physics A: Mathematical & Theoretical, 42 (2009) 012001, Oct 2008
Abstract: We calculate the average of two characteristic polynomials for the real Ginibre ensemble of asymmetric random matrices, and its chiral counterpart. Considered as quadratic forms they determine a skew-symmetric kernel from which all complex eigenvalue correlations can be derived. Our results are obtained in a very simple fashion without going to an eigenvalue representation, and are completely new in the chiral case. They hold for Gaussian ensembles which are partly symmetric, with kernels given in terms of Hermite and Laguerre polynomials respectively, depending on an asymmetry parameter. This allows us to interpolate between the maximally asymmetric real Ginibre and the Gaussian Orthogonal Ensemble, as well as their chiral counterparts.
URI: http://bura.brunel.ac.uk/handle/2438/2776
ISSN: http://fr.arxiv.org/abs/0810.1458
http://dx.doi.org/10.1088/1751-8113/42/1/012001
Appears in Collections:Mathematical Physics
Dept of Mathematics Research Papers

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