Syllabus:
- Definition of a Markov chain.
- Basic properties.
- Powers of the transition matrix.
- Communicating classes.
- Hitting times.
- Strong Markov property.
- Transience and recurrence.
- Random walks on $\mathbb{Z}^d$.
- Invariant distribution.
- Time reversibility.
- Convergence to equilibrium.
- Ergodic theorem.