Probability density of determinants of random matrices

Giovanni M. Cicuta (1, 2) , Madan Lal Mehta (3)

1 Dipartimento di Fisica [Parma]
2 INFN - Istituto Nazionale di Fisica Nucleare, Sezione di Milano
3 SPhT - Service de Physique Théorique

In this brief paper the probability density of a random real, complex and quaternion determinant is rederived using the singular values. The behaviour of suitably rescaled random determinants is studied in the limit of infinite order of the matrices.

Domains: Condensed Matter [cond-mat]

Giovanni M. Cicuta, Madan Lal Mehta. Probability density of determinants of random matrices. Journal of Physics A: Mathematical and General (1975 - 2006), 2000, ⟨10.1088/0305-4470/33/45/302⟩. ⟨cea-02904781⟩