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Distribution of the determinant of a random real-symmetric matrix from the Gaussian orthogonal ensemble

Abstract : The Mellin transform of the probability density of the determinant of N X N 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.
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https://hal.archives-ouvertes.fr/hal-01127733
Contributor : Renaud Delannay Connect in order to contact the contributor
Submitted on : Sunday, March 8, 2015 - 9:07:20 AM
Last modification on : Saturday, October 16, 2021 - 11:22:03 AM

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Renaud Delannay, Gérard Le Caër. Distribution of the determinant of a random real-symmetric matrix from the Gaussian orthogonal ensemble. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2000, 62 (2), pp.1526-1536. ⟨10.1103/PhysRevE.62.1526⟩. ⟨hal-01127733⟩

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