Correlations for parameter-dependent random matrices

Abstract

Correlations for parameter-dependent Gaussian random matrices, intermediate between symmetric and Hermitian and antisymmetric Hermitian and Hermitian, are calculated. The (dynamical) density-density correlation between eigenvalues at different values of the parameter is calculated for the symmetric to Hermitian transition and the scaled N → ∞ limit is computed. For the antisymmetric Hermitian to Hermitian transition the equal-parameter n-point distribution function is calculated and the scaled limit computed. A circular version of the antisymmetric Hermitian to Hermitian transition is formulated. In the thermodynamic limit the equal-parameter distribution function is shown to coincide with t..