In 1931 Erwin Schroedinger asked for the most likely path of diffusive particles that is in agreement with empirical marginals at two end-points in time. In essence, he sought a new probability law on the space of paths which is consistent with the observed empirical marginals (assuming that the prior law, the Wiener measure, is not). His solution is now known as the Schroedinger bridge. Similar questions can be raised in the context of Markov chains, quantum evolutions (over non-commutative probability spaces), densities of inertial particles obeying Langevin dynamics, and also the evolution of state-densities of dynamical systems in general. In the talk we will explain the Schroedinger bridge problem and its solution for Markov chains and Quantum channels.
The presentation will be based on joint work with Michele Pavon (Padova).
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