Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited
Emmanuel Cépa, Dominique Lépingle (2010)
ESAIM: Probability and Statistics
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The Brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices is interpreted as a system of interacting Brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). We prove...