Random matrices, random polynomials and Coulomb systems

Details Random matrices, random polynomials and Coulomb systems Random matrices, random polynomials and Coulomb systems

1999-11-15

arxiv.org/abs/cond-mat/9911222v1

J. Phys. IV France 10 (2000) Pr5-45 -- Pr5-52

Physics

Condensed Matter

Statistical Mechanics

8 pages, to appear in the Proceedings of the International Conference on Strongly Coupled Coulomb Systems, Saint-Malo, 1999

Scientific paper

It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special attention devoted to electrostatic analogies. We also discuss the joint probability density of the zeros of polynomials whose coefficients are complex Gaussian variables. This leads to a new two-dimensional solvable gas of interacting particles, with non-trivial interactions between particles.

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