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December 2021 Asymptotic analysis for extreme eigenvalues of principal minors of random matrices
T. Tony Cai, Tiefeng Jiang, Xiaoou Li
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Ann. Appl. Probab. 31(6): 2953-2990 (December 2021). DOI: 10.1214/21-AAP1668

Abstract

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×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.

Funding Statement

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.

Citation

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T. Tony Cai. Tiefeng Jiang. Xiaoou Li. "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

Information

Received: 1 July 2019; Revised: 1 August 2020; Published: December 2021
First available in Project Euclid: 13 December 2021

Digital Object Identifier: 10.1214/21-AAP1668

Subjects:
Primary: 60B20 , 60F99
Secondary: 60K35

Keywords: Extremal eigenvalues , maximum of random variables , minimum of random variables , Random matrix

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.31 • No. 6 • December 2021
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