Markov Chains and Mixing Times

Markov chains are a fundamental concept in probability theory and stochastic processes. They consist of a sequence of random variables representing a process that transitions from one state to another in a way that depends only on the current state, not on the history of how that state was reached. This memoryless property is characteristic of Markov processes. ### Key Concepts of Markov Chains: 1. **States**: The possible configurations or conditions in which the process can exist.