Localization Schemes

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" summary

Introduces a framework that turns mixing-time proofs into two tasks: pick a localization scheme and prove approximate conservation of variance or entropy along its martingale of measures. Presents three concrete schemes: coordinate-by-coordinate localization (recovers spectral-independence Poincaré bounds), Eldan’s stochastic localization on R^n (reduces Ising sampling in the uniqueness regime to product measures and yields a modified Log-Sobolev bound O(1/n) when ||J||op ≤ 1/2), and a Poisson-driven negative fields localization that handles the hardcore model in the tree-uniqueness regime.

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" chapters (7)

1. 0:00Localization schemes intro
2. 12:21What is localization scheme
3. 20:18Variance evolution analysis
4. 34:56Stochastic localization beyond cube
5. 42:31Localization for Ising models
6. 49:45Negative fields in hardcore model
7. 54:28Summary and open problems

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