Cheeger's Inequalities

This lecture covers the concept of Cheeger's inequalities for random walks on graphs, focusing on the Lovasz-Simonovits curve and the Cheeger-type inequalities. It explains the relationship between the Cheeger constant and the conductance of a graph, illustrating how to find poorly expanding sets using local algorithms. The lecture also delves into the proof of Cheeger's inequalities and their implications for bipartite components. Additionally, it discusses the convergence properties of random walks based on the signs of certain parameters, providing insights into threshold cuts and the behavior of random walks in different scenarios.