Expected Number of Visits in State

This lecture discusses the criterion for recurrence in infinite chains based on the expected number of visits in a state. The instructor explains the propositions and proofs related to the recurrence and transience of states in the context of Markov chains. The lecture covers the concept of recurrence, transient states, and the convolution relation between probabilities. Various lemmas and examples are provided to illustrate the expected number of visits in different states. The lecture concludes with remarks on the expected number of visits in a state and examples of simple random walks in different dimensions.