  Wigner-type randomizations of the tangent spaces of classical symmetric
spaces can be thought of as ordinary Wigner matrices on which additional
symmetries have been imposed. In particular, they fall within the scope of a
framework, due to Schenker and Schulz-Baldes, for the study of fluctuations of
Wigner matrices with additional dependencies among their entries. In this
contribution, we complement the results of these authors in that we develop a
calculus of patterns which makes it possible to control the asymptotic
contributions of dihedral non-crossing pair partitions for the Cartan classes
DIII and CI, thus obtaining explicit CLTs for these cases.
