Fisher-Rao Gradient Flow: Geodesic Convexity and Functional Inequalities

ArXi:2407.15693v2 Announce Type: replace-cross The dynamics of probability density functions have been extensively studied in computational science and engineering to understand physical phenomena and facilitate algorithmic design. Of particular interest are dynamics formulated as gradient flows of energy functionals under the Wasserstein metric. The development of functional inequalities, such as the log-Sobole inequality, plays a pivotal role in analyzing the convergence of these dynamics.