Markov chains are a type of mathematical model that describe a sequence of possible events in which the probability of each event depends only on the outcome of the previous event. They are commonly used in various areas of research, such as probability theory, statistics, and computer science, to model random processes and analyze systems with a series of interconnected states or events. In a Markov chain, each state represents a possible outcome, and the transition probabilities between states indicate the likelihood of moving from one state to another. These probabilities are typically specified in a transition matrix, which captures the dynamics of the system over time. Markov chains can be used to predict future states, estimate long-term behavior, and analyze the stability and convergence of a system. Overall, Markov chains are a powerful tool for modeling and analyzing complex systems with stochastic behavior, making them a valuable research area in a wide range of disciplines.