Sharp Bounds on Eigenvalues via Spectral Embedding Based on Signless Laplacians

Here is the Journal Page. The arXiv page is here. It could also be downloaded here.

Abstract

Using spectral embedding based on the probabilistic 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 Overis Gharan, 2018].