| 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) |
