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Dimension-free concentration on Gaussian space
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Classroom Contents
Ronen Eldan- Revealing the Simplicity of High-Dimensional Objects via Pathwise Analysis
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- 1 Intro
- 2 Emergence of a simple structure in high-dimensional settings
- 3 Dimension-free concentration on Gaussian space
- 4 Gaussian-like behavior beyond the Gaussian measure
- 5 High dimensional convexity and the KLS conjecture
- 6 Pure state decompositions of interacting particle systems
- 7 Martingale techniques - a simple illustration
- 8 A Pathwise approach
- 9 Analysis of variance
- 10 Stochastic Localization (discrete version)
- 11 Basic properties of
- 12 Time-derivatives correspond to spatial moments
- 13 Emergence of a Gaussian
- 14 Collapsing into localized measures
- 15 Some applications
- 16 Application #4: Concentration on the discrete hypercube
