  We study the problem of identification of linear dynamical system from a
single trajectory, via excitations of isotropic Gaussian. In stark contrast
with previously reported results, Ordinary Least Squares (OLS) estimator for
even \emph{stable} dynamical system contains non-vanishing error in \emph{high
dimensions}; which stems from the fact that realizations of non-diagonalizable
dynamics can have strong \emph{spatial correlations} and a variance, of order
$O(e^{n})$, where $n$ is the dimension of the underlying state space. Employing
\emph{concentration of measure phenomenon}, in particular tensorization of
\emph{Talagrands inequality} for random dynamical systems we show that observed
trajectory of dynamical system of length-$N$ can have a variance of order
$O(e^{nN})$. Consequently, showing some or most of the $n$ distances between an
$N-$ dimensional random vector and an $(n-1)$ dimensional hyperplane in
$\mathbb{R}^{N}$ can be close to zero with positive probability and these
estimates become stronger in high dimensions and more iterations via
\emph{Isoperimetry}. \emph{Negative second moment identity}, along with
distance estimates give a control on all the singular values of \emph{Random
matrix} of data, revealing limitations of OLS for stable non-diagonalizable and
explosive diagonalizable systems.
