Quaternion determinant expressions for multilevel dynamical correlation functions of parametric random matrices

Parametric random matrix ensembles which describe the transition among diff erent matrix symmetries are studied. In the case of the transition to the h ermitian symmetry, exact expressions for dynamical correlation functions am ong many eigenvalues at different times are shown to have quaternion determ inant forms. (C) 1999 Elsevier Science B.V. All rights reserved.