Flows in the space of probability measures and convergence of Wigner transforms

Friday, July 24, 2009 - 9:00am - 9:50am
EE/CS 3-180
Luigi Ambrosio
We provide an extension of the theory of flows in Euclidean spaces associated to wekly differentiable
velocity fields, replacing the Euclidean state space with the space of probability measure. This way, the
continuity equation can be viewed as an ODE in the space of probability measures and we provide some
well-posedness and stability results. We illustrate, as an example and a basic motivation for the development
of the theory, the problem of convergence of Wigner transforms in Quantum Mechanics.