Moments of the characteristic polynomial in the three ensembles of random matrices - Archive ouverte HAL Access content directly
Journal Articles Journal of Physics A: Mathematical and General (1975 - 2006) Year : 2001

Moments of the characteristic polynomial in the three ensembles of random matrices

(1) , (1)
1

Abstract

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.
Fichier principal
Vignette du fichier
MehNor.pdf (126.04 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

cea-02904765 , version 1 (22-07-2020)

Identifiers

Cite

Madan Lal Mehta, Jean-Marie Normand. Moments of the characteristic polynomial in the three ensembles of random matrices. Journal of Physics A: Mathematical and General (1975 - 2006), 2001, 34 (22), pp.4627-4639. ⟨10.1088/0305-4470/34/22/304⟩. ⟨cea-02904765⟩
30 View
74 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More