Distribution of the determinant of a random real-symmetric matrix from the Gaussian orthogonal ensemble
Delannay, Renaud ; Le Caër, Gérard
HAL, hal-01127733 / Harvested from HAL
Text on HAL
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.
Publié le : 2000-08-04
Classification:  MODELS,  EIGENVALUES,  PROBABILITY,  FLUCTUATIONS,  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] 
@article{hal-01127733,
     author = {Delannay, Renaud and Le Ca\"er, G\'erard},
     title = {Distribution of the determinant of a random real-symmetric matrix from the Gaussian orthogonal ensemble},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01127733}
}

Delannay, Renaud; Le Caër, Gérard. Distribution of the determinant of a random real-symmetric matrix from the Gaussian orthogonal ensemble. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-01127733/