A Generalized Plasma and Interpolation Between Classical Random Matrix Ensembles

Abstract

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 β=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 β=1 and 4 circular ensemble, and an exactly solvable two-component generalized plasma which interpolates between β=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 (k1+k2)-point correlation function in a Pfaffian form. Crucial to our working is an identity which expresses the Va..