Lectures

  1. Mon 29 Oct
    • Introduction and course outline.
    • Transition matrix and initial distribution of a Markov chain.
      (LPW Sec 1.1, Numerical example: Frog.R)
  2. Tue 30 Oct
    • Left-multiplication and right-multiplication by the transition matrix.
      (LPW Rem 1.3)
    • Random walks on graphs.
      (LPW Sec 1.4, 1.5.1)
    • Random walk on the hypercube: The Hamming weight and Ehrenfest's urn.
      (LPW Sec 2.3)
  3. Mon 5 Nov
    • Reachability of states and hitting times.
      (LPW Sec 1.5.2)
    • Random mapping presentation.
      (LPW Sec. 1.2)
    • Simulation of the initial distribution. Random number generation.
      (LPW App. B.3; RANDOM.ORG)
  4. Tue 6 Nov (Computer lab at Room MaD353)
  5. Mon 12 Nov
    • Existence of a stationary distribution.
      (LPW Sec 1.5.1, 1.5.3; Warning: Section 1.5 contains some errors).
    • Uniqueness of the stationary distribution.
      (LPW Sec 1.5.4, LPW Exercise 1.13)
  6. Tue 13 Nov
    • Reversible Markov chains.
      (LPW Sec. 1.6)
    • Birth-and-death processes.
      (LPW Sec. 2.5)
  7. Mon 19 Nov
    • Total variation distance.
      (LPW Sec 4.1)
    • Coupling of random variables.
      (LPW Sec 4.2)
  8. Tue 20 Nov
    • Aperiodic Markov chains.
      (LPW Sec 1.3)
    • Markov chain convergence theorem.
      (LPW Sec 4.3)
  9. Mon 26 Nov
    • Graph coloring and counting problems.
      (LPW Sec 3.1)
    • Markov chain Monte Carlo: Metropolis algorithm.
      (LPW 3.2)
  10. Tue 27 Nov
    • Mixing times and coalescing chains.
      (LPW Sec 4.4–4.5)
    • Glauber dynamics and Gibbs samplers.
      (LPW Sec 3.3)
    • Decentralized graph coloring.
      K. Duffy, C. Bordenave, D. Leith : Decentralized constraint satisfaction
  11. Mon 3 Dec (No lecture)
  12. Tue 4 Dec (Full afternoon from 14:15–17:30, Room MaD302)