Sun Dec 14, 1:30-4:30pm AEDT.
This tutorial presents the localization method to prove inequalities in high dimension, pioneered by
Lovász and Simonovits (1993), and its stochastic extension developed by Eldan (2012). The method has found applications in a surprising variety of settings, from the original motivation of isoperimetric inequalities to optimization, concentration of measure and to bounding the mixing rate of Markov chains, both discrete and continuous. At heart, the method converts a given inequality (for a set or distribution) in high dimension to a highly structured instance, typically just one-dimensional. The tutorial and accompanying survey article include several examples.
The first part of the tutorial introduces a rich family of inequalities from diverse areas, describes the classical (or standard) localization method and illustrates its application to deriving some of these inequalities. The focus of the second part is the more general stochastic localization approach, providing the necessary technical tools with examples and outlining its recent applications.
Survey on Localization (with Yunbum Kook; comments welcome!)
| 1:30-3pm | Part I: Classical Localization (notes) | 3-3:30pm | break |
| 3:30-4:30pm | Part II: Stochastic Localization |