Tail bounds for gaps between eigenvalues of sparse random matrices
Probability
2020-12-21 v3
Abstract
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 error probability from the work of the second author and Vu. As an application of our tail bounds, we show that for sparse Erd\H{o}s--R\'enyi graphs, weak and strong nodal domains are the same, answering a question of Dekel, Lee, and Linial.
Cite
@article{arxiv.1901.05948,
title = {Tail bounds for gaps between eigenvalues of sparse random matrices},
author = {Patrick Lopatto and Kyle Luh},
journal= {arXiv preprint arXiv:1901.05948},
year = {2020}
}
Comments
Addressed referee suggestions. Simplified some aspects of the proof