Topics in Probability -
Markov Chains and Mixing Times
Fall 2007/8
Teachers
Ori Gurel-Gurevich and Ariel Yadin (under supervision of Gady Kozma).
Time and Location
The course takes place at Ziskind 1 on Sundays 14-16 (while the strike lasts)
Syllabus
This course deals with following topics:
- Markov Chains, irreducibility and aperiodicity
- Stationary distribution, existence and uniqueness
- Total variation norm, Convergence to the stationary distribution
- Mixing times
- Methods for bounding the mixing time
Lecture notes
These are our own lecture notes for the course. They are to be considered incomplete, erroneous and outdated. Use at you own Risk!
Part 1 - Introduction (updated 02/12/07): ps,pdf, dvi.
Exercises: ps, pdf, dvi
Part 2 - Stationary distribution, existence and uniqueness (updated 27/12/07): ps, pdf, dvi.
Exercises: ps, pdf, dvi
Part 3 - Convergence to stationary distribution (updated 27/12/07): ps, pdf, dvi.
Exercises: ps, pdf, dvi
Resources
This course will mainly follow the book "Markov Chains and Mixing Times" by Levin, Peres and Wilmer, the URL for which was given in class.
