Correlation matrix of equi-correlated normal population: fluctuation of the largest eigenvalue, scaling of the bulk eigenvalues, and stock market
等相关正态总体的相关矩阵：最大特征值波动、谱主体缩放与股票市场
Given an $N$-dimensional sample of size $T$ and form a sample correlation matrix $\mathbf{C}$. Suppose that $N$ and $T$ tend to infinity with $T/N $ converging to a fixed finite constant $Q>0$. If the population is a factor model, then the eigenvalue distribution of $\mathbf{C}$ almost surely converges weakly to Marčenko-Pastur distribution such that the index is $Q$ and the scale parameter is the limiting ratio of the specific variance to the $i$-th variable $(i\to\infty)$.…