Mathematical Physics Calculation of a Certain Determinant

Madan Lal Mehta (1) , Rong Wang (2)

1 SPhT - Service de Physique Théorique
2 CAS - Chinese Academy of Sciences [Beijing]

The $n×n$ determinant det[($a+j −i$) ($b+j +i$)] is evaluated. This completes the calculation of the Mellin transform of the probability density of the determinant of a random quaternion self-dual matrix taken from the gaussian symplectic ensemble. The inverse Mellin transform then gives the later probability density itself.

Domaines: Physique mathématique [math-ph]

Madan Lal Mehta, Rong Wang. Mathematical Physics Calculation of a Certain Determinant. Communications in Mathematical Physics, 2000, 214, pp.227 - 232. ⟨10.1007/s002200000260⟩. ⟨cea-02904796⟩