  In this work, we study non-asymptotic bounds on correlation between two time
realizations of stable linear systems with isotropic Gaussian noise.
Consequently, via sampling from a sub-trajectory and using \emph{Talagrands'}
inequality, we show that empirical averages of reward concentrate around steady
state (dynamical system mixes to when closed loop system is stable under linear
feedback policy ) reward , with high-probability. As opposed to common belief
of larger the spectral radius stronger the correlation between samples,
\emph{large discrepancy between algebraic and geometric multiplicity of system
eigenvalues leads to large invariant subspaces related to system-transition
matrix}; once the system enters the large invariant subspace it will travel
away from origin for a while before coming close to a unit ball centered at
origin where an isotropic Gaussian noise can with high probability allow it to
escape the current invariant subspace it resides in, leading to
\emph{bottlenecks} between different invariant subspaces that span
$\mathbb{R}^{n}$, to be precise : system initiated in a large invariant
subspace will be stuck there for a long-time: log-linear in dimension of the
invariant subspace and inversely to log of inverse of magnitude of the
eigenvalue. In the problem of Ordinary Least Squares estimate of system
transition matrix via a single trajectory, this phenomenon is even more evident
if spectrum of transition matrix associated to large invariant subspace is
explosive and small invariant subspaces correspond to stable eigenvalues. Our
analysis provide first interpretable and geometric explanation into intricacies
of learning and concentration for random dynamical systems on continuous, high
dimensional state space; exposing us to surprises in high dimensions
