论文标题
由布朗运动驱动的高维矩阵过程的特征值分布
Eigenvalue distributions of high-dimensional matrix processes driven by fractional Brownian motion
论文作者
论文摘要
在本文中，我们研究了经验频谱分布的高维行为$ \ {l_n（t），t \ in [0，t] \} $，用于一类$ n \ times n $ symmetric/symmetian/hermitian随机矩阵，其条目的条目是由随机差异方程式通过fractaction brownian brownian $ hurst parameter of hurst paramers of hurst paramers的溶液产生的（1）。对于Wigner-type矩阵，我们获得了$ \ {l_n（t），t \ in [0，t] \} _ {n \ in \ Mathbb n} $ in $ c（[0，T]，\ Mathbf P（\ Mathbb r）$ scute in \ Cite in \ cite2010};对于WishArt-Type矩阵，我们获得了$ \ {l_n（t），t \ in [0，t] \} _ {n \ in \ mathbb n} $ on $ c（[0，t]，\ mathbf p（\ mathbf p（\ mathb r））$ y appendenty in appendenty cromptige croment cromptige crestix prognix prognity cromptignix priffectix， $ \ {l_n（t），t \ in [0，t] \} $作为$ n \ to \ infty $的极限也被表征。
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.
