Reversible Chains & Detailed Balance

This lecture covers the concept of reversible chains and detailed balance in ergodic Markov chains. It explains the conditions for a chain to be reversible and the equation that must be satisfied for detailed balance. Examples and counter-examples are provided to illustrate these concepts, including scenarios where the detailed balance equation cannot be met. The lecture also discusses the properties of cyclic random walks and the transition probabilities in such systems. Additionally, it explores the state of chains involving numbered balls in urns, detailing the transition probabilities and the application of detailed balance in these scenarios.