Foundations of Markov Chains: Mixing, Hitting, and Cover Times

Analyzing how random processes move and stabilize is central to probability theory, computer science, and data modeling. This course provides a structured introduction to Markov chains, focusing on the fundamental relationships between mixing times, hitting times, and cover times. You will build an intuitive and mathematical understanding of how states transition, how fast systems reach equilibrium, and how long random walks take to explore state spaces. What you'll learn: - Understand foundational definitions, transition matrices, and stationary distributions in Markov chains - Calculate hitting times, commute times, and total cover times across various network structures - Evaluate total variation distance and measure how quickly a chain converges toward equilibrium - Explore modern connections between maximal hitting times on large subsets and mixing times - Apply coupling techniques and spectral methods to establish bounds on convergence rates - Practice analyzing random walks on graphs through step-by-step written examples and exercises The course begins with core terminology and probability basics before guiding you through analytical methods and modern equivalence theorems. It is designed for beginners in probability theory, mathematics, and computer science who want a solid grounding in stochastic processes without prior advanced prerequisites. Begin reading today to deepen your understanding of Markov chains and random walks.