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Spin Systems (Cont.)
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Classroom Contents
Rapid Mixing of Glauber Dynamics up to Uniqueness via Contraction
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- 1 Intro
- 2 Hardcore Model = Weighted Independent Sets
- 3 Sampling from Hardcore Model
- 4 Uniqueness Threshold
- 5 Glauber Dynamics A classic, simple Markov Chain Monte Carlo (MCMC) method In each step: 1. Pick a vertex v uniformly at random 2. Update a conditioned on all other vertices
- 6 Known Results (Ferromagnetic)
- 7 Known Results (Antiferromagnetic)
- 8 Spin Systems The hardcore model and Ising model belong to the family of 2-spin systems
- 9 Spin Systems (Cont.)
- 10 Up-to-A Uniqueness
- 11 Proof Approach
- 12 Self-Avoiding Walk Tree
- 13 Example
- 14 Influences on SAW Tree (Cont.)
- 15 Conclusion
