Markov Chain Analysis

This lecture introduces the concept of Markov chains through a detailed analysis of a specific example involving two fleas moving in opposite directions with different rates. The instructor explains the transition matrix, eigenvalues, and eigenvectors of the system, leading to the calculation of probabilities at different time points. By applying the quadratic formula and deriving the probabilities for various states, the lecture demonstrates the convergence of probabilities and the importance of eigenvectors in determining the system's behavior.