Theory Seminar - Spectral Independence in High-Dimensional Expanders, Kuikui Liu
Paul G. Allen School via YouTube
Overview
Syllabus
Intro
A Natural Algorithm
Spectral Independence (cont.)
Application: The Hardcore Model
Why care about the Hardcore Model?
A Physical Phase Transition
A Complexity Phase Transition
Outline
Simplicial Complex from u
X for the Hardcore Model
Markov Chain Decomposition
Proof Strategy
Garland's Method for Local Spectral Expansion
Weak Spatial Mixing
Spatial Mixing and Spectral Independence on zd
Rough Strategy
The Tree Recurrence
Bounding Each Vertex Separately
Induction on Levels
Open-Ended Problems
Open Problems for Hardcore Model
Taught by
Paul G. Allen School