Bernoulli Lecture by James R. Lee - Information-optimal drifts and the geometry of Markov processes   03 December 2015

If one records a Markov process converging to stationarity from an initial distribution and then plays the video in reverse, what appears is a new (time inhomogeneous) Markov process that constructs the initial distribution using as little information as possible.

One can leverage this entropic optimality to study the behavior of the random walk, especially at "early" times. For some problems, this perspective appears to offer something new over semi-group methods. We discuss applications to regularizing properties of classical diffusion operators and to functional inequalities on finite graphs and groups. There are interesting connections to discrete analogs of non-negative Ricci curvature.
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