  We extend the relation between random matrices and free probability theory
from the level of expectations to the level of fluctuations. We introduce the
concept of "second order freeness" and derive the global fluctuations of
Gaussian and Wishart random matrices by a general limit theorem for second
order freeness. By introducing cyclic Fock space, we also give an operator
algebraic model for the fluctuations of our random matrices in terms of the
usual creation, annihilation, and preservation operators. We show that
orthogonal families of Gaussian and Wishart random matrices are asymptotically
free of second order.
