  In this article, we study high-dimensional behavior of empirical spectral
distributions $\{L_N(t), t\in[0,T]\}$ for a class of $N\times N$
symmetric/Hermitian random matrices, whose entries are generated from the
solution of stochastic differential equation driven by fractional Brownian
motion with Hurst parameter $H \in(1/2,1)$. For Wigner-type matrices, we obtain
almost sure relative compactness of $\{L_N(t), t\in[0,T]\}_{N\in\mathbb N}$ in
$C([0,T], \mathbf P(\mathbb R))$ following the approach in \cite{Anderson2010};
for Wishart-type matrices, we obtain tightness of $\{L_N(t),
t\in[0,T]\}_{N\in\mathbb N}$ on $C([0,T], \mathbf P(\mathbb R))$ by tightness
criterions provided in Appendix \ref{subset:tightness argument}. The limit of
$\{L_N(t), t\in[0,T]\}$ as $N\to \infty$ is also characterised.
