Lecture: Diffusions and Random Walks as Robust Eigenvectors

Last time, we talked about electrical networks, and we saw that we could reproduce some of the things we have been doing with spectral methods with more physically intuitive techniques. These methods are of interest since they are typically more robust than using eigenvectors and they often lead to simpler proofs. Today, we will go into more detail about a similar idea, namely whether we can interpret random walks and diffusions as providing robust or regularized or stable analogues of eigenvectors. Many of the most interesting recent results in spectral graph methods adopt this approach of using diffusions and random walks rather than eigenvectors. We will only touch on the surface of this approach.