Global fluctuations in general β Dyson's Brownian motion

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:118

Article

Bender, Martin

关键词: central limit theorem;    Dyson's Brownian motion;    interacting diffusion;    random matrices;   

DOI  :  10.1016/j.spa.2007.07.010

来源: Elsevier

【 摘 要 】

We consider a system of diffusing particles on the real line in a quadratic external potential and with a logarithmic interaction potential. The empirical measure process is known to converge weakly to a deterministic measure-valued process as the number of particles tends to infinity. Provided the initial fluctuations are small, the rescaled linear statistics of the empirical measure process converge in distribution to a Gaussian limit for sufficiently smooth test functions. For a large class of analytic test functions, we derive explicit general formulae for the mean and covariance in this central limit theorem by analyzing a partial differential equation characterizing the limiting fluctuations. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free