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See, for example, these lecture notes, or, for a more formal exposition, consult Levinson's Algorithm, Wold's Decomposition, and Spectral Estimation by A. Papoulis (1985).


If you allow the Hankel matrix to be rectangular, then there is a paper saying that the re-normalized leading singular values of Hankel matrix converge to the energy of the high energy state.


$\newcommand\R{\mathbb R}$You want to find $\ln M_W(t)$, where $M_W$ is the moment generating function (mgf) of $W$, given by \begin{equation*} M_W(t)=E e^{tW}=\sum_{n=0}^\infty\frac{t^n EW^n}{n!} \end{equation*} for real $t$. By obvious rescaling, without loss of generality $\sigma=1$. For natural $n$, \begin{equation*} W^n=|v|^{2(n-1)} vv^\top, \...

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