  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.
