5 papers
Regional Stability and New Eigenvalue Perturbation Bounds
Phuc Tran, Van Vu
Let be an symmetric matrix with eigenvalues . Let , where is a symmetric noise matrix, and denote the eigenvalues of $\tild…
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…
New matrix perturbation bounds with relative strength: 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 spectr…
Matrix perturbation bounds via contour bootstrapping
Phuc Tran, Van Vu
Matrix perturbation bounds play an essential role in the design and analysis of spectral algorithms. In this paper, we use a "contour bootstrapping" argument to derive several new…
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…