| Issue |
J. Phys. IV France
Volume 10, Number PR5, March 2000
The 1999 International Conference on Strongly Coupled Coulomb Systems
|
|
|---|---|---|
| Page(s) | Pr5-45 - Pr5-52 | |
| DOI | https://doi.org/10.1051/jp4:2000506 | |
The 1999 International Conference on Strongly Coupled Coulomb Systems
J. Phys. IV France 10 (2000) Pr5-45-Pr5-52
DOI: 10.1051/jp4:2000506
Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, bâtiment 100, 91405 Orsay cedex, France
© EDP Sciences 2000
J. Phys. IV France 10 (2000) Pr5-45-Pr5-52
DOI: 10.1051/jp4:2000506
Random matrices, random polynomials and Coulomb systems
P. LeboeufLaboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, bâtiment 100, 91405 Orsay cedex, France
Abstract
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