Joint stochastic localization and applications
Researchers have developed a new framework called joint stochastic localization, extending existing pathwise analysis techniques for high-dimensional probability and sampling. This framework unifies and characterizes existing processes under Eldan's $\alpha$-scheme, introducing a joint scheme that couples probability measures using shared Brownian motion. The resulting Eldan's $\alpha$-distance offers a novel way to measure distances between probability measures, with theoretical properties analyzed and efficient estimators developed for specific cases. AI