K. Luh

activity

20112022

most citedMartingale Couplings and Bounds on the Tails of Probability Distributions

1 citations · 2 across the 5 of their papers we have counts for

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7 papers · 1 filter

math.PR2022

Eigenvalue Gaps of Random Perturbations of Large Matrices

Kyle Luh, Ryan Vogel, Alan Yu

The current work applies some recent combinatorial tools due to Jain to control the eigenvalue gaps of a matrix $M_{n} = M + N_{n}$ where $M$ is deterministic, symmetric with large ope…

math.PR2020

Eigenvectors and controllability of non-Hermitian random matrices and directed graphs

Kyle Luh, Sean O'Rourke

We study the eigenvectors and eigenvalues of random matrices with iid entries. Let $N$ be a random matrix with iid entries which have symmetric distribution. For each unit eigenvec…

math.PR2019

Tail bounds for gaps between eigenvalues of sparse random matrices

Patrick Lopatto, Kyle Luh

We prove the first eigenvalue repulsion bound for sparse random matrices. As a consequence, we show that these matrices have simple spectrum, improving the range of sparsity and er…

math.PR2018

Eigenvector Delocalization for Non-Hermitian Random Matrices and Applications

Kyle Luh, Sean O'Rourke

Improving upon results of Rudelson and Vershynin, we establish delocalization bounds for eigenvectors of independent-entry random matrices. In particular, we show that with high pr…

math.PR2018

Sparse Random Matrices have Simple Spectrum

Kyle Luh, Van Vu

Let $M_{n}$ be a class of symmetric sparse random matrices, with independent entries $M_{ij} = δ_{ij} ξ_{ij}$ for $i \leq j$ . $δ_{ij}$ are i.i.d. Bernoulli random variables taking th…

math.PR2015★ 1 cited

Dictionary Learning with Few Samples and Matrix Concentration

Kyle Luh, Van Vu

Let $A$ be an $n \times n$ matrix, $X$ be an $n \times p$ matrix and $Y = A X$ . A challenging and important problem in data analysis, motivated by dictionary learning and other prac…