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| - Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited
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| Abstract
| - The Brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices N x 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 measure-valued process exists and is the unique solution of a deterministic second-order PDE. The uniform law on [-π;π] is the only limiting distribution of µ t when t goes to infinity and µ t has an analytical density.
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| - © EDP Sciences, SMAI, 2001
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