Markov Chains 2021

Milton Jara
Last updated: 03/01/2021

Teaching Assistant: Lucas Arag√£o

Written notes will be available HERE. The material on the notes will be discussed on online meetings, with emphasis on examples and applications. The link for the lectures will appear HERE before each class. Note that neither the material on the written notes nor the online meetings will be self-contained and it should be taken as an extended syllabus. The students are expected to complete their study, before and after each lecture, with a bibliography of their choice. Some suggested choices are

  • D. Levin, Y. Peres and E. Wilmer; Markov Chains and Mixing Times.
  • J. Norris; Markov Chains.
  • D. Aldous, J. Fill; Reversible Markov Chains and Random Walks on Graphs


The only requirement for this course is a basic course on probability. In particular, familiarity with concepts like independence and conditional probability is important. Basic linear algebra and/or calculus could be useful, but not essential. No measure theory is required.

Oral examinations

Evaluation will be based on oral examinations. Before each online meeting, a few students will be selected at random for an oral examination. All students must be present at that time, since no shows will count as a failed exam. Also, every two Mondays there will be longer oral examinations, based on exercises posted on Fridays.

T.A. meetings

T.A. meetings will be held online. The link for the meeting will appear HERE.


  • 18/01, study sheet HERE