Eigenvalue gaps of the Laplacian of random graphs
Probability
2025-03-18 v2 Combinatorics
Abstract
We show that, with very high probability, the random graph Laplacian has simple spectrum. Our method provides a quantitatively effective estimate of the spectral gaps. Along the way, we establish results on affine no-gaps delocalization, no-structure delocalization, overcrowding and small entries of the eigenvectors for the Laplacian model. These findings are of independent interest.
Cite
@article{arxiv.2501.00234,
title = {Eigenvalue gaps of the Laplacian of random graphs},
author = {Nicholas Christoffersen and Kyle Luh and Hoi H. Nguyen and Jingheng Wang},
journal= {arXiv preprint arXiv:2501.00234},
year = {2025}
}
Comments
30 pages