Journal article

Analogies between random matrix ensembles and the one-component plasma in two-dimensions

Peter J Forrester



The eigenvalue PDF for some well known classes of non-Hermitian random matrices - the complex Ginibre ensemble for example - can be interpreted as the Boltzmann factor for one-component plasma systems in two-dimensional domains. We address this theme in a systematic fashion, identifying the plasma system for the Ginibre ensemble of non-Hermitian Gaussian random matrices G, the spherical ensemble of the product of an inverse Ginibre matrix and a Ginibre matrix G1-1G2, and the ensemble formed by truncating unitary matrices, as well as for products of such matrices. We do this when each has either real, complex or real quaternion elements. One consequence of this analogy is that the leading for..

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University of Melbourne Researchers


Awarded by Australian Research Council

Funding Acknowledgements

This research was supported by the Australian Research Council grant DP140102613. I thank Jesper Ipsen for useful feedback relating on an earlier draft. Further, I thank Dong Wang and Jac Verbaarschot at NUS, and the Simons Center for Geometry and Physics (program on Random Matrices, fall semester 2015) respectively, for their hospitality and arranging financial support during my study leave period when ideas for the present paper were being formulated.