Davis-Kahan Theorem under a moderate gap condition
Numerical Analysis
2025-10-28 v1 Numerical Analysis
Spectral Theory
Statistics Theory
Statistics Theory
Abstract
The classical Davis-Kahan theorem provides an efficient bound on the perturbation of eigenspaces of a matrix under a large (eigenvalue) gap condition. In this paper, we consider the case when the gap is moderate. Using a bootstrapping argument, we obtain a new bound which is efficient when the perturbation matrix is uncorrelated to the ground matrix. We believe that this bound is sharp up to a logarithmic term.
Keywords
Cite
@article{arxiv.2510.22393,
title = {Davis-Kahan Theorem under a moderate gap condition},
author = {Phuc Tran and Van Vu},
journal= {arXiv preprint arXiv:2510.22393},
year = {2025}
}