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arXiv · 1012.0597

A generalized plasma and interpolation between classical random matrix ensembles

Peter J. Forrester·Christopher D. Sinclair
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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.

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Peter J. Forrester, Christopher D. Sinclair. 2010-12-02. A generalized plasma and interpolation between classical random matrix ensembles. https://doi.org/10.1007/s10955-011-0173-3

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