| Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
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Course: Special Topics - Probability Instructor: Yogeshwaran D / Mathew Joseph Room: G26 Level: Postgraduate Time: Currently offered |
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| Syllabus Past Exams Syllabus: Pre-Requisites : Introduction to Markov chains, some measure-theoretic probability and basics of mixing times. Recap of Markov Chains and Mixing Times, Spectral Methods for Mixing Times, Coupling and Path Coupling, Entropy Methods and Log-Sobolev Inequalities. Recent advances : Spectral independence and basis exchange walk, Stochastic localization and comparison with spectral independence. Discrete curvature and relation to mixing times. Suggested Texts : (a) J. Salez. Mixing times for Markov chains. https://www.ceremade.dauphine.fr/~salez/mix.pdf (b) P. Caputo. Lecture notes on entropy and Markov chains http://www.mat.uniroma3.it/users/caputo/entropy.pdf (c) D. Stefankovic and E. Vigoda. Lecture Notes on Spectral Independence and Bases of a Matroid: Local-to-Global and Trickle-Down from a Markov Chain Perspective https://arxiv.org/abs/2307.13826 (d) Y. Chen and R. Eldan. Localization Schemes: A Framework for Proving Mixing Bounds for Markov Chains. https://arxiv.org/abs/2203.04163v2 (e) P. Caputo and J. Salez. Entropy factorization via curvature. https://arxiv.org/abs/2407.13457 Evaluation:
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