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We consider eigenvalues of generalized Wishart processes as well as particlesystems, of which the empirical measures converge to deterministic measures asthe dimension goes to infinity. In this paper, we obtain central limit theoremsto characterize the fluctuations of the empirical measures around the limitmeasures by using stochastic calculus. As applications, central limit theoremsfor the Dyson's Brownian motion and the eigenvalues of the Wishart process arerecovered under slightly more general initial conditions, and a central limittheorem for the eigenvalues of a symmetric Ornstein-Uhlenbeck matrix process isobtained.

High-dimensional central limit theorems for eigenvalue distributions of generalized Wishart processes