J. Phys. IV France 10 (2000) Pr5-45-Pr5-52
Random matrices, random polynomials and Coulomb systemsP. Leboeuf
Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, bâtiment 100, 91405 Orsay cedex, France
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.
© EDP Sciences 2000