Before revision: I apply the method of planar diagrammatic expansion  to solve the problem of finding the mean spectral density of the  non-Hermitian time-lagged covariance estimator for a system of i.i.d. Gaussian random variables .
After revision: I apply the method of planar diagrammatic expansion to solve the problem of finding the mean spectral density of the Hermitian equal-time and non-Hermitian time-lagged covariance estimator for a system of i.i.d. Gaussian random variables .