This is the course website for Entropy and Markov Chains offered in Spring 2025 at ISI Bangalore. The course will assume a basic introduction to Markov chains along with understanding of some measure-theoretic probability and mixing times.
Recap of Markov Chains and Mixing Times
Spectral Methods for Mixing Times
Coupling and Path Coupling
Entropy Methods and Log-Sobolev Inequalities
Spectral independence and basis exchange walk
Stochastic localization and comparison with spectral independence.
Discrete curvature and relation to mixing times.
The exact timings will be updated one week before each lecture. However, we will try to stick to the following schedule:
Tuesday 3:30-:4:30pm
Friday 3:30-4:30pm
We will mostly follow the following references
J. Salez, Mixing times for Markov chains. Lecture Notes.
P. Caputo, Lecture notes on entropy and Markov chains. Lecture Notes.
P. Caputo and J. Salez, Entropy factorization via curvature. 2024.
T. Ceccherini-Silberstein, F. Scarabotti and F. Tolli . Harmonic Analysis on Finite Groups: Representation Theory, Gelfand Pairs and Markov Chains. Cambridge University Press; 2008.
E. Nestoridi, S. Olesker-Taylor. Limit profiles for reversible Markov chains. Probab. Theory Relat. Fields. 2022.
Y. Chen, R. Eldan. Localization Schemes: A Framework for Proving Mixing Bounds for Markov Chain ; Extended Abstract
Chen Talk Video , Slides ; Eldan Talk 1, Talk 2.
Notes on Stochastic Localization [To be uploaded].
Imre Csiszar and Janos Korner, Information Theory, Cambridge
Speakers:
Srivatsa Balaji
Shubham Ovhal
Other Participants:
All the lectures were held offline at G26 Classroom of Indian Statistical Institute, Bangalore.