Overview
Syllabus
Intro
Hardcore Model = Weighted Independent Sets
Sampling from Hardcore Model
Uniqueness Threshold
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
Known Results (Ferromagnetic)
Known Results (Antiferromagnetic)
Spin Systems The hardcore model and Ising model belong to the family of 2-spin systems
Spin Systems (Cont.)
Up-to-A Uniqueness
Proof Approach
Self-Avoiding Walk Tree
Example
Influences on SAW Tree (Cont.)
Conclusion
Taught by
IEEE FOCS: Foundations of Computer Science