Principal minors of Gaussian orthogonal ensemble
Probability
2024-02-14 v2
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.
Keywords
Cite
@article{arxiv.2205.05732,
title = {Principal minors of Gaussian orthogonal ensemble},
author = {Renjie Feng and Gang Tian and Dongyi Wei and Dong Yao},
journal= {arXiv preprint arXiv:2205.05732},
year = {2024}
}