Controlling Uncertainty

Our account begins in 1931/1932, when one of the fathers of quantum theory, Erwin Schroedinger, proposed a Gedankenexperiment to comprehend the propagation of a cloud of Brownian particles. He proposed [1], [2] the inference problem to identify the most likely evolution of a large collection of particles as they traverse between two endpoints in timeâ their distribution being measured and available at the two endpoints. This random evolution, now known as the Schroedinger bridge, entails a flow of one-time distributions that interpolate the known initial and final marginals.