New tools for optimal mixing of Markov chains: Spectral independence
and entropy decay
Lectures
New: Lecture Notes on Spectral Independence (including Random Walk Theorem via Dirichlet form/Variance perspective)
Pietro Caputo: Markov chain fundamentals:
Lecture video
and Lecture notes
Entropy tensorization:
Lecture video
and Lecture notes
Comprehensive notes from Pietro Caputo
Tali Kaufman:
Intro to simplicial complexes and Local to Global theorems:
Lecture notes
Nima Anari:
Matroids and bases exchange walk:
Lecture video
and Lecture notes
Heng Guo:
Entropy decay for bases exchange walk:
Lecture video
Kuikui Liu:
Spectral independence and optimal mixing:
Lecture video
and Lecture notes
Heng Guo: Tutte polynomial:
Lecture video
Zongchen Chen:
Correlation decay, zero-freeness, and spectral independence:
Lecture video and Lecture notes
Nima Anari:
Domain sparsification and average-case local-to-global:
Lecture video