  In this paper we study the global fluctuations of block Gaussian matrices
within the framework of second-order free probability theory. In order to
compute the second-order Cauchy transform of these matrices, we introduce a
matricial second-order conditional expectation and compute the matricial
second-order Cauchy transform of a certain type of non-commutative random
variables. As a by-product, using the linearization technique, we obtain the
second-order Cauchy transform of non-commutative rational functions evaluated
on selfadjoint Gaussian matrices.
