Spectrums of random Gaussian $g$-cyclic matrices

The paper deals with $g$-cyclic matrices $X_n$, which are determined by a random vector $(x(0),\dots,x(n-1))$ having a normal distribution with zero mean and covariance matrix of a special kind. In the case $g=1$, the joint distribution of eigenvalues $\lambda_0,\dots,\lambda_{n-1}$ of $X_n$ is found. In a more general case, the limiting spectral function of $\lambda_0,\dots,\lambda_{n-1}$ is obtained.