Lectures

The lectures are given Tue 10:15–12:00 in Room MaD302 and Wed 10:15–12:00 in Room MaD380.

  1. Tue 1 Nov
    • Introduction and course outline.
    • Transition matrix and initial distribution of a Markov chain.
      (Häggström Ch2)
  2. Wed 2 Nov
    • Simple random walk on a graph
    • Reachability of states (can a MC starting at state i reach state j?)
      (Häggström Ch4)
  3. Tue 8 Nov
    • Simulation of Markov chains: random number generators
      (RANDOM.ORG)
    • Initiation function and update function of a Markov chain
      (Häggström Ch3)
  4. Thu 10 Nov (Room MaD353)
  5. Tue 15 Nov
    • (Ir)reducible Markov chains
      (Häggström Ch4)
    • (A)periodic Markov chains
      (Häggström Ch4)
  6. Wed 16 Nov
    • Strong irreducibility
      (Häggström Cor 4.1)
    • Mean hitting times
      (Häggström Lem 5.1)
  7. Tue 22 Nov
    • Existence of a stationary distribution
      (Häggström Thm 5.1)
    • Collision Lemma: Independent irreducible aperiodic finite MC's will eventually collide
      (Häggström p. 35–36, inside the proof of Thm 5.2)
  8. Wed 23 Nov
    • Total variation metric
      (Häggström Def 5.2)
    • Markov Chain convergence theorem
      (Häggström Thm 5.2 & Thm 5.3)
  9. Tue 29 Nov
    • Reversible Markov chains
      (Häggström Ch 6)
    • Simple random walk on an undirected graph
      (Häggström Ex 6.1)
    • Metropolis algorithm
      (Häggström Ch 7; Levin, Peres & Wilmer Sec 3.2)
  10. Wed 30 Nov
    • Modeling optimal scheduling problems using hardcore particle configurations (a.k.a. independent sets in graph theory)
    • A Gibbs sampler (a.k.a. Glauber chain) for generating feasible hardcore configurations
      (Häggström Example 7.2)
    • Randomized optimization algorithms using low-temperature Boltzmann distributions (a.k.a. Gibbs measures)
      (Häggström Theorem 13.1)