In this paper, 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 $C([0,T],P(ℝ))$ following the approach in [1]; for Wishart-type matrices, we obtain tightness of ${\{L_N(t),t\in [0,T]\}}_{N\in \mathbb{N}}$ on $C([0,T],P(ℝ))$ by tightness criterions provided in Appendix B. The limit of $\{L_N(t),t\in [0,T]\}$ as $N\to \infty$ is also characterized.

在本文中，我们研究了一类 $N\times N$ 对称/厄米特随机矩阵的经验谱分布 $\{L_N(t),t\in [0,T]\}$ 的高维行为，其条目是由随机微分方程驱动的解生成的通过具有 Hurst 参数 $H\in (1/2,1)$ 的分数布朗运动。对于维格纳型矩阵，按照[1]中的方法，我们在 $C([0,T],P(ℝ))$ 中获得了几乎确定的 ${\{L_N(t),t\in [0,T]\}}_{N\in \mathbb{N}}$ 的相对紧性；对于Wishart型矩阵，我们通过附录B中提供的紧度准则获得 ${\{L_N(t),t\in [0,T]\}}_{N\in \mathbb{N}}$ 对 $C([0,T],P(ℝ))$ 的紧度。 $\{L_N(t),t\in [0,T]\}$ 的极限为 $N\to \infty$ 也是有特点的。