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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 that a limiting...
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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