EIGENVECTOR CORRELATIONS IN THE COMPLEX GINIBRE ENSEMBLE

• 成果类型: Article
• 署名作者: Crawford, Nicholas; Rosenthal, Ron
• 署名单位: Technion Israel Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1746
• 发表日期: 2022
• 页码: 2706-2754
• 关键词: circular law; RANDOM MATRICES; statistics; real

摘要

The complex Ginibre ensemble is the distribution of an N x N nonHermitian random matrix over C with i.i.d. complex Gaussian entries normalized to have mean zero and variance 1/N. Unlike the Gaussian unitary ensemble, for which the eigenvectors are distributed according to Haar measure on the compact group U (N), independently of the eigenvalues, the geometry of the eigenbases of the Ginibre ensemble are not particularly well understood. In this paper we systematically study properties of eigenvector correlations in this matrix ensemble. In particular, we uncover an extended algebraic structure which describes their asymptotic behavior (as N goes to infinity). Our work extends previous results of Chalker and Mehlig (Phys. Rev. Lett. 81 (1998) 3367-3370), in which the correlation for pairs of eigenvectors was computed.