Optimal mass transport

Wednesday, August 16, 2017 - 10:00am - 10:45am
Jin Feng (University of Kansas)
In 2006, Tom Kurtz and I co-authored a book on a Hamilton-Jacobi approach to the Large deviation theory for Markov processes. An important step is to prove the uniqueness of a limiting Hamilton-Jacobi PDE. I will outline this approach in the beginning part of this talk. Then I give a few examples, including one open problem in statistical mechanics. A characteristic difficulty of the open problem is an invariance relation.
Friday, January 29, 2016 - 10:15am - 11:05am
Optimal mass transport (OMT) provides a natural geometry for interpolating distributions (displacement interpolation) and modeling flows. As such it has been the cornerstone of many recent developments in physics, probability theory, image processing, time-series analysis, and systems and control. An alternative framework, rooted in statistical mechanics and large deviations, is that of Schrödinger bridges (entropic interpolation) which can in fact be seen as a stochastic regularization of OMT.
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