Before revision: I apply the method of planar diagrammatic expansion - introduced in a self-consistent way - to solve the problem of finding the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, for systems of Gaussian random variables with various underlying covariance functions, both writing the general equations and applying them to several toy models.
After revision: I apply the method of planar Gaussian diagrammatic expansion is applied to find the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged cross-covariance estimators, for systems of Gaussian random variables with various underlying covariance functions, both writing the general equations and applying them to several toy models.