  We consider eigenvalues of generalized Wishart processes as well as particle
systems, of which the empirical measures converge to deterministic measures as
the dimension goes to infinity. In this paper, we obtain central limit theorems
to characterize the fluctuations of the empirical measures around the limit
measures by using stochastic calculus. As applications, central limit theorems
for the Dyson's Brownian motion and the eigenvalues of the Wishart process are
recovered under slightly more general initial conditions, and a central limit
theorem for the eigenvalues of a symmetric Ornstein-Uhlenbeck matrix process is
obtained.

Probability