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 \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. The exact evaluation of the general correlation is used to exhibit a perfect screening sum rule.
Cite
@article{arxiv.1012.0597,
title = {A generalized plasma and interpolation between classical random matrix ensembles},
author = {Peter J. Forrester and Christopher D. Sinclair},
journal= {arXiv preprint arXiv:1012.0597},
year = {2015}
}
Comments
21 pages