T. Sahlsten: Analysis, Random Walks and Groups, lecture notes. Update 9.1.2023: I have included now dice rolling to the notes. Now the notes should be complete for the course, but I may still fix any errors, typos etc. if anything emerges. Please send me any comments if you find something. Update 19.1.2023: Minor typo fixes in the proofs of the Section 3.4 (taking powers of 2 in Lemma 3.29). Update 2.2.2023: added details on representation theory of the symmetric group, including S_3. Update 9.2.2023: Included more details on the characters and how they are used to prove the trace lemma needed for Placherel's theorem. Update 15.2.2023: Included the proof of the Heisenberg Uncertainty Principle we did in the lectures.
These contain essentially everything done in the course, and you can follow these if you miss a lecture. The only topic not covered in the videos is the dice rolling added to lecture notes in 2023 version of this course.
Further material
(introduction and beginning): P. Diaconis: Group Representations in Probability and Statistics, IMS Lecture Series volume 11, Institute of Mathematical Statistics, Hayward, California, 1988
(beginning of the book): F. Ceccherini-Silberstein, T. Scarabotti, F. Tolli: Harmonic Analysis on Finite Groups. Cambridge University Press, 2008.