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Brownian particles with electrostatic repulsion on the circle : Dyson’s model for unitary random matrices revisited

Emmanuel Cépa;  Dominique Lépingle — 2001

ESAIM: Probability and Statistics

The brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices N × N is interpreted as a system of N 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 N goes to infinity (through the empirical measure process). We prove that a limiting...

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

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 that a...

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