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 (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. The exact evaluation of the general correlation is used to exhibit a perfect screening sum rule.

21 pages

References in corpus (3)

• The Ginibre ensemble of real random matrices and its scaling limits
• Ensemble Averages when βis a Square Integer
• A Solvable Mixed Charge Ensemble on the Line: Global Results

Cited by in corpus (5)

• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• A geometrical triumvirate of real random matrices
• The Partition Function of Multicomponent Log-Gases
• Classical skew orthogonal polynomials in a two-component log-gas with charges $+1$ and $+2$
• Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $\beta =2$