Sharp Bounds on Eigenvalues via Spectral Embedding Based on Signless Laplacians

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].