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Wigner-type randomizations of the tangent spaces of classical symmetricspaces can be thought of as ordinary Wigner matrices on which additionalsymmetries have been imposed. In particular, they fall within the scope of aframework, due to Schenker and Schulz-Baldes, for the study of fluctuations ofWigner matrices with additional dependencies among their entries. In thiscontribution, we complement the results of these authors in that we develop acalculus of patterns which makes it possible to control the asymptoticcontributions of dihedral non-crossing pair partitions for the Cartan classesDIII and CI, thus obtaining explicit CLTs for these cases.

Fluctuations of Wigner-type random matrices associated with symmetric spaces of class DIII and CI