2001/01/31 by M. L. Mehta, Mehta, M. L., J. -M. Normand +1
Chemistry · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Molecular spectroscopy and chirality #Random Matrices and Applications #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0101469
tex, 1 file, 15 pages [SPhT-T01/016], published J. Phys. A: Math. Gen. 34 (2001) 1-13
arxiv created 2001/05/23 · arxiv updated 2009/11/30
Moments of the characteristic polynomial of a random matrix taken from any of the three ensembles, orthogonal, unitary or symplectic, are given either as a determinant or a pfaffian or as a sum of determinants. For gaussian ensembles comparing the two expressions of the same moment one gets two remarkable identities, one between an n× n determinant and an m× m determinant and another between the pfaffian of a 2n× 2n anti-symmetric matrix and a sum of m× m determinants.