Can you please help me find the distribution of eigenvalues of a Toeplitz matrix $\mathbf{K}$ that is constructed as follows: $\mathbf{K}=\left[ \begin{array}{cccc} 1 & \rho & \ldots & \, \, \rho^{N-1} \\ \rho & 1 & \ldots & \, \,\rho^{N-2}\\ \vdots & \vdots & \ddots & \vdots \\ \rho^{N-1} & \rho^{N-2} & \ldots & 1 \\ \end{array} \right].$ where $0 \leq \rho < 1$.
Thanks a lot in advance,
Farzad