SES # TOPICS 1 Introduction to Finite Markov Chains (PDF) 2 Markov Chains: Stationary Distribution (PDF) 3 Markov Chains: Time-reversal (PDF) 4 Introduction to Markov Chain Mixing (PDF) 5 Stationary Times (PDF) 6 Lower Bounds on Mixing Times (PDF) 7 Summary on Mixing Times (PDF) 8 Random Walk on Networks 1 (PDF) 9 Random Walk on Networks 2 (PDF) 10 Hitting Times (PDF) 11 Summary on Random Walk on Networks (PDF) 12 Countable State Space Chain 1 (PDF) 13 Countable State Space Chain 2 (PDF) 14 Midterm Exam (No Lecture Notes) 15 Conditional Expectation and Introduction to Martingales (PDF) 16 Martingales: Optional Stopping Theorem (PDF) 17 Martingales: Convergence (PDF) Almost Sure Convergence (PDF) 18 Martingales: Uniformly Integrable (PDF) 19 Galton-Watson Tree (PDF) 20 Poisson Process (PDF) 21 Continuous Time Markov Chain (PDF) 22 Infinitesimal Generator (PDF) 23 Irreducible and Recurrence (PDF) 24 Stationary Distribution (PDF)