3 papers
math.SP2026
New matrix perturbation bounds with relative norm: Perturbation of eigenspaces
Phuc Tran, Van Vu
Matrix perturbation bounds (such as Weyl and Davis-Kahan) are used abundantly in many areas of mathematics and data science. Many bounds (such as the above two) involve the spectra…
math.NA2025
Davis-Kahan Theorem under a moderate gap condition
Phuc Tran, Van Vu
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 th…
math.CO2025
A short proof of Kahn-Kalai conjecture
P. Tran, V. Vu
In a recent paper, Park and Pham famously proved Kahn-Kalai conjecture. In this note, we simplify their proof, using an induction to replace the original analysis. This reduces the…