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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

• Function : Author
Jean-Marie Normand
• Function : Author

#### 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.

#### Domains

Physics [physics] Mathematical Physics [math-ph]

### Dates and versions

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

### Identifiers

• HAL Id : cea-02904765 , version 1
• DOI :

### 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⟩

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