### 数学学院、所2019年系列学术活动（第141场）：姜铁锋 教授 明尼苏达大学双城校区

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 $m \times m$ 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 to compressed sensing in signal processing and high dimensional linear regression in statistics. This is a joint work with Tony Cai and Xiaoou Li.