Birth and Death Chains

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Covers Markov chains, coupled chains, and their applications, emphasizing the importance of irreducibility.

Covers the fundamentals of regular expressions and includes exercises on defining languages.

Explores the coupling of Markov chains and the proof of the ergodic theorem, emphasizing distribution convergence and chain properties.

Introduces the basics of finite automata, including deterministic and non-deterministic types, regular expressions, and acceptance criteria.

Covers Markov chains decomposition, LLN proof, Inventory Model application, and average costs.

Discusses the sharp transition in mixing time of a random walk.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Covers the fundamentals of finite automata and formal languages.

Explains the proof of the ergodic theorem and the concept of positive-recurrence in Markov chains.

Covers the theory of Markov chains, focusing on reversible chains and detailed balance.