Distribution of the determinant of a random real-symmetric matrix from the gaussian orthogonal ensemble
The Mellin transform of the probability density of the determinant of NxN random real-symmetric matrices from the Gaussian orthogonal ensemble is calculated. The determinant probability density is given by a single Meijer G function for odd N. The distribution of the potential at the origin, within the Coulomb gas interpretation, is investigated from the Mellin transform of the determinant distribution and is shown to be asymptotically Gaussian.
Delannay
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Groupe Matiere Condensee et Materiaux, CNRS UMR No. C6626, Universite de Rennes-I, Avenue du General Leclerc, F-35042 Rennes Cedex, France.
Le Caer G