5 papers
Extreme principal minors of Wishart and deformed GOE matrices
Zhaorui Dong, Tiefeng Jiang, Tuan Pham +1
We study the laws of large numbers for the largest eigenvalues among all principal minors of Wishart matrices and deformed GOE matrices. We propose a new method based on identifyin…
Limiting spectral distributions of large consistent rank correlation matrices
Zhaorui Dong, Fang Han, Jianfeng Yao
We study random matrices whose entries are obtained by applying consistent rank correlations, such as Hoeffding's , pairwise to a high-dimensional random vector with mutually in…
Quadratic form of heavy-tailed self-normalized random vector with applications in -heavy Marčenko--Pastur law
Zhaorui Dong, Johannes Heiny, Jianfeng Yao
Let be a random vector with i.i.d.\ real-valued components in the domain attraction of an -stable law with , and let $\mathbf{y}=\mathbf{x}/\|\mathbf…
Spectral analysis of large dimensional Chatterjee's rank correlation matrix
Zhaorui Dong, Fang Han, Jianfeng Yao
This paper studies the spectral behavior of large dimensional Chatterjee's rank correlation matrix when observations are independent draws from a high-dimensional random vector wit…
Towards Quantifying the Hessian Structure of Neural Networks
Zhaorui Dong, Yushun Zhang, Jianfeng Yao +1
Empirical studies reported that the Hessian matrix of neural networks (NNs) exhibits a near-block-diagonal structure, yet its theoretical foundation remains unclear. In this work,…