Work

Principal minors of Gaussian orthogonal ensemble

Year: 2025

Type: article

Abstract: In this paper, we study the extremal process of the maxima of all the largest eigenvalues of principal minors of the classical Gaussian orthogonal ensemble (GOE). We prove that the fluctuation of the maxima is given by the Gumbel distribution in the limit. We also derive the limiting joint distribution of the maxima and the corresponding eigenvector, which implies that these two random variables are asymptotically independent.

Source: Forum Mathematicum

DOI: 10.1515/forum-2025-0307

Authors: Renjie Feng, Gang Tian, Dongyi Wei, Dong Yao

Institutions: The University of Sydney, Peking University, Jiangsu Normal University

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

Funders: National Natural Science Foundation of China, National Key Research and Development Program of China