A generalized plasma and interpolation between classical random matrix ensembles

Understand

The eigenvalue probability density functions of the classical random matrix ensembles have a well known analogy with the one component log-gas at the special couplings \beta = 1,2 and 4.

• It has been known for some time that there is an exactly solvable two-component log-potential plasma which interpolates between the \beta =1 and 4 circular ensemble, and an exactly solvable two-component generalized plasma which interpolates between \beta = 2 and 4 circular ensemble.
• We extend known exact results relating to the latter --- for the free energy and one and two-point correlations --- by giving the general (k_1+k_2)-point correlation function in a Pfaffian form.
• Crucial to our working is an identity which expresses the Vandermonde determinant in terms of a Pfaffian.