Controlling Uncertainty

Our account begins in 1931/1932, when one of the fathers of quantum theory, Erwin Schrodinger, 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 time- their distribution being measured and available at the two endpoints. This random evolution, now known as the Schrodinger bridge, entails a flow of one-time distributions that interpolate the known initial and final marginals.