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The Tree Recurrence
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Classroom Contents
Theory Seminar - Spectral Independence in High-Dimensional Expanders, Kuikui Liu
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- 1 Intro
- 2 A Natural Algorithm
- 3 Spectral Independence (cont.)
- 4 Application: The Hardcore Model
- 5 Why care about the Hardcore Model?
- 6 A Physical Phase Transition
- 7 A Complexity Phase Transition
- 8 Outline
- 9 Simplicial Complex from u
- 10 X for the Hardcore Model
- 11 Markov Chain Decomposition
- 12 Proof Strategy
- 13 Garland's Method for Local Spectral Expansion
- 14 Weak Spatial Mixing
- 15 Spatial Mixing and Spectral Independence on zd
- 16 Rough Strategy
- 17 The Tree Recurrence
- 18 Bounding Each Vertex Separately
- 19 Induction on Levels
- 20 Open-Ended Problems
- 21 Open Problems for Hardcore Model
