Sharp Bounds on Eigenvalues via Spectral Embedding Based on Signless Laplacians
arXiv:2111.08777 · doi:10.1016/j.jfa.2022.109799
Abstract
Using spectral embedding based on the signless Laplacian, we obtain bounds on the spectrum of transition matrices on graphs. As a consequence, we bound return probabilities and the uniform mixing time of simple random walk on graphs. In addition, spectral embedding is used in this article to bound the spectrum of graph adjacency matrices. Our method is adapted from [Lyons and Oveis Gharan, 2017].
In this version, some literature are cited more properly; contributions therein are mentioned in a more appropriate way. Especially, Proposition 3.8 was first published in [Mao & Song, 2013]; we are only giving a different approach in this submission