Global fluctuations in general [beta] Dyson's Brownian motion

Martin Bender

Stochastic Processes and their Applications, 2008, vol. 118, issue 6, 1022-1042

Abstract: 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.

Keywords: Central; limit; theorem; Dyson's; Brownian; motion; Interacting; diffusion; Random; matrices (search for similar items in EconPapers)
Date: 2008
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