Sharp bounds on eigenvalues via spectral embedding based on signless Laplacians

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 Oveis Gharan [13].(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

Using spectral embedding based on the probabilistic signless Laplacian, this article provides bounds on the spectrum of transition matrices on graphs. These bounds lead to constraints on return probabilities and uniform mixing time of simple random walk on graphs. In addition, spectral embedding is used to bound the spectrum of graph adjacency matrices. The method used in this article is adapted from Lyons and Oveis Gharan [13].