Localization Schemes

Explore the concept of localization schemes in analyzing Markov chain mixing times for continuous space and discrete hypercube models in this lecture by Yuansi Chen from Duke University. Delve into the process of assigning probability measures to martingales that localize in space over time, and discover how this approach simplifies mixing time analysis by transforming complex distributions into more manageable ones. Examine the connection between localization schemes and high-dimensional concentration and convex geometry. Study Eldan's stochastic localization on Euclidean space and its application to sampling Ising models in the uniqueness regime on discrete hypercubes. Investigate the differences between discrete and continuous spaces in this context, and learn about new Poisson-process-driven negative fields localization schemes for analyzing Glauber dynamics in sampling the hardcore model.