BROWNIAN PARTICLES WITH ELECTROSTATIC REPULSION ON THE CIRCLE: DYSON'S MODEL FOR UNITARY RANDOM MATRICES REVISITED
BROWNIAN PARTICLES WITH ELECTROSTATIC REPULSION ON THE CIRCLE: DYSON'S MODEL FOR UNITARY RANDOM MATRICES REVISITED
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DOI：
10.1051/ps:2001109
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
E. Cépa;D. Lépingle
中科院分区：
文献类型：
--
作者：
E. Cépa;D. Lépingle
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 dene the nite 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 innity (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 ( ;) is the only limiting distribution of t when t goes to innity and t has an analytical density.
