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 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 to compressed sensing in signal processing and high-dimensional linear regression in statistics.
The research of Tony Cai was supported in part by NSF Grants DMS-1712735 and DMS-2015259 and NIH Grants R01-GM129781 and R01-GM123056. Tiefeng Jiang’s research was supported by NSF Grants DMS-1406279 and DMS-1916014. Xiaoou Li was partially supported by NSF Grant DMS-1712657.
"Asymptotic analysis for extreme eigenvalues of principal minors of random matrices." Ann. Appl. Probab. 31 (6) 2953 - 2990, December 2021. https://doi.org/10.1214/21-AAP1668