论文标题
部分可观测时空混沌系统的无模型预测
Edge Universality of Sparse Random Matrices
论文作者
论文摘要
我们考虑稀疏随机矩阵的极端特征值的统计数据，这是一类随机矩阵，其中包括ERD {\ h o} s-r {é} nyi Graph $ g（n，p）$的归一化邻接矩阵。最近，Lee显示了直到明确的随机偏移，如果平均度随图形的大小增长，$ pn> n^\ varepsilon $，则极端特征值的最佳刚度。我们在同一制度中证明了（i）对于明确的随机度量，所有特征值的最佳刚性均具有最佳刚度。 （ii）直到显式随机移位，极端特征值的波动被赋予了tracy-widom分布。
We consider the statistics of the extreme eigenvalues of sparse random matrices, a class of random matrices that includes the normalized adjacency matrices of the Erd{\H o}s-R{é}nyi graph $G(N,p)$. Recently, it was shown by Lee, up to an explicit random shift, the optimal rigidity of extreme eigenvalues holds, provided the averaged degree grows with the size of the graph, $pN>N^\varepsilon$. We prove in the same regime, (i) Optimal rigidity holds for all eigenvalues with respect to an explicit random measure. (ii) Up to an explicit random shift, the fluctuations of the extreme eigenvalues are given the Tracy-Widom distribution.
