Asymptotic Analysis for Extreme Eigenvalues of Principal Minors of Random Matrices
Tony Cai, Tiefeng Jiang, and Xiaoou Li
Consider a standard white Wishart matrix with parameters n and p. Motivated by applications in high-dimensional statistics and signal processing, we perform asymptotic analysis on the maxima and minima of the eigenvalues of all the m by m principal minors, under the asymptotic regime that n, p, m go to infinity. Asymptotic results concerning extreme eigenvalues of principal minors of real Wigner matrices are also obtained. In addition, we discuss an application of the theoretical results to the construction of compressed sensing matrices, which provides insights in high dimensional linear regression.