ASYMPTOTIC ANALYSIS FOR EXTREME EIGENVALUES OF PRINCIPAL MINORS OF RANDOM MATRICES

• 成果类型: Article
• 署名作者: Cai, T. Tony; Jiang, Tiefeng; Li, Xiaoou
• 署名单位: University of Pennsylvania; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1668
• 发表日期: 2021
• 页码: 2953-2990
• 关键词: restricted isometry property; statistical-theory; energy-levels; largest entries; distributions; RECOVERY; limit; UNIVERSALITY; ensembles; coherence

摘要

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 x 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.